I think that we have it well-established (regardless of whether or not one sees this as flawed logic) that Harry is not a horcrux. A horcrux has to be made intentionally, and the recipient is cursed and classified as an "evil object," etc. Neither of which is true for Harry - so, as stated by JKR herself, Harry is not a horcrux as such.

But the fact remains that murder can, in fact, accidentally create something that shares a key property of the horcrux: the soul splits, attaches itself to the nearest recipient, and lingers inside. As it does in Harry's case.

So my question is: is this only true for wizards? A muggle cannot utilize a spell to create a horcrux. But, if a horcrux-like object / being can be created accidentally through murder without intentional horcrux-creating spells, can this also happen in the case of a Muggle committing murder?

Can a Muggle commit murder, have their soul split, and have the piece of the soul inadvertently attach itself to something nearby without any horcrux-creating spell being cast?

Probably not.

I only say probably instead of straight up no because i cant find a really revealing quote on it, but it is for sure that Horcruxes can be made from non-magic murder, i.e the diary.

The diary dates back to when Voldemort was still Tom Marvolo Riddle. After opening the Chamber of Secrets, he used the Basilisk to kill Myrtle Warren, providing the murder necessary to craft a Horcrux.
_{- Everyone you didn’t realise was connected to Voldemort’s Horcruxes - Pottermore}

I consider this non-magic because of the lack of a wand, some people might argue that he used parslemouth and somehow link that to magic but i disagree.

It is referred to as a Magic-Creation.

"Of the Horcrux, wickedest of magical inventions, we shall not speak nor give direction —"
_{- Horcrux - Harry Potter Wiki}

Now this is a quote from the book but i dont have a copy on me at the moment.
And this is another one.

"While the magical container is still intact, the bit of soul inside it can flit in and out of someone if they get too close to the object. I don’t mean holding it for too long... I mean close emotionally. Ginny poured her heart out into that diary, she made herself incredibly vulnerable. You’re in trouble if you get too fond of or dependent on the Horcrux."
_{- Horcrux - Harry Potter Wiki}

This quote leads me to believe there is some magic involved after the murder. And now that i've read @Alex's answer this quote seems to support that.

"By an act of evil — the supreme act of evil. By commiting murder. Killing rips the soul apart. The wizard intent upon creating a Horcrux would use the damage to his advantage: He would encase the torn portion —"

This to me seems like there needs to be some sort of magic transfer from wherever the piece of soul is floatin' around to some sort of container.

It seems that there are two distinct stages of damaging the soul. The mere act of murder is said to rip apart the soul. This is what Slughorn tells Tom Riddle in Chapter Twenty Three of Half-Blood Prince:

"By an act of evil — the supreme act of evil. By commiting murder. Killing rips the soul apart. The wizard intent upon creating a Horcrux would use the damage to his advantage: He would encase the torn portion —"

And this is what Dumbledore indicates to Snape in Chapter Thiirty Three of Deathly Hallows:

“If you don’t mind dying,” said Snape roughly, “why not let Draco do it?”

“That boy’s soul is not yet so damaged,” said Dumbledore. “I would not have it ripped apart on my account.”

Muggles can presumably achieve the state of having a ripped apart soul, as they can commit murder just like wizards can. However, Dumbledore's statement in Chapter Thirty Five of Deathly Hallows about Harry being a "Horcrux" is very specific:

“You were the seventh Horcrux, Harry, the Horcrux he never meant to make. He had rendered his soul so unstable that it broke apart when he committed those acts of unspeakable evil, the murder of your parents, the attempted killing of a child. But what escaped from that room was even less than he knew. He left more than his body behind. He left part of himself latched to you, the would-be victim who had survived.

This implies that Voldemort had gone beyond the mere ripping apart that happens to anyone who murders. By creating previous Horcruxes, Voldemort had rendered his soul entirely unstable.

Hermione's statement in Chapter Six of Deathly Hallows also implies that it is specifically the act of creating Horcruxes that makes the soul so unstable:

“And the more I’ve read about them,” said Hermione, “the more horrible they seem, and the less I can believe that he actually made six. It warns in this book how unstable you make the rest of your soul by ripping it, and that’s just by making one Horcrux!”

If this is true, then Muggles should not be able to qualify for the inadvertent "Horcrux" situation. This is because even though they can rip apart their souls by murdering, they can't render their souls entirely unstable by making other Horcruxes (as that requires a spell).

Additionally, the piece of Voldemort's soul seems to have only latched on to Harry because Voldemort couldn't die (because of his other Horcruxes). But if someone who could die was in the same situation, they would just die. If the mere fact that they murdered would be enough to keep them alive then all murderers would be immortal (at least until whoever possesses their soul dies), something which we do not find in any of the books.

Or perhaps put differently: When a regular murderer (with no prior Horcruxes) gets killed he simply dies. Even though his soul has been ripped apart because of the murder, there is nothing tethering his soul to this world, so his soul would simply do what anyone's soul does when they die. However, if someone had a prior Horcrux then when he gets killed he won't die, because the Horcrux is tethering his soul to this world. In such a case there could be the potential for a piece of his soul to break off and latch on to another living being. However, it still seems that this would not happen to someone who only had one Horcrux. It seems from Dumbledore's statement that Voldemort's soul was especially unstable because of the multiple Horcruxes.

In any case, this shouldn't be able to happen to a Muggle because a Muggle wouldn't have a prior Horcrux to tether his soul to this world.

From PotterCast’s JK Rowling Interview (quoted below) we know that creating a Horcrux needs to be done intentionally and requires (Dark) magic. The only reason that part of Voldemort's soul was able to leave his body and attach to Harry was because he had done the process so many times, each destabilizing his soul further, and then was hit with the backfiring of his own Killing Curse:

Here is the thing: for convenience, I had Dumbledore say to Harry, "You were the Horcrux he never meant to make," but I think, by definition, a Horcrux has to be made intentionally. So because Voldemort never went through the grotesque process that I imagine creates a Horcrux with Harry, it was just that he had destabilized his soul so much that it split when he was hit by the backfiring curse. And so this part of it flies off, and attaches to the only living thing in the room. A part of it flees in the very-close-to-death limbo state that Voldemort then goes on and exists in. I suppose it's very close to being a Horcrux, but Harry did not become an evil object. He didn't have curses upon him that the other Horcruxes had. He himself was not contaminated by carrying this bit of parasitic soul.

[...]

I do think that the strict definition of "Horcrux," once I write the [Harry Potter Encyclopedia], will have to be given, and that the definition will be that a receptacle is prepared by Dark Magic to become the receptacle of a fragmented piece of soul, and that that piece of soul was deliberately detached from the master soul to act as a future safeguard, or anchor, to life, and a safeguard against death.

Because creating a Horcrux needs to be done intentionally and requires magic, a muggle would not be able to do it accidentally. They would not be able to destabilize their soul enough without creating a Horcrux either, nor would they be likely to be hit with the rebound of a Killing Curse.