Dobby (probably) killed him.
The final mention of Pettigrew in the original script (and in the film) is when you see him collapse, having been zapped from behind by Dobby.
[The knob turns and light splashes into the cellar as ...... Wormtail fills the doorway]
[Harry and Ron stiffen, then watch Wormtail fall forward, stiff as a board, tumbling in a heavy heap on the cement floor below. They turn back as Dobby appears, Wormtail’s wand in his tiny fist.]
DOBBY: Who gets his wand?
In the absence of anything to suggest otherwise, I think we can say that it's likely that Dobby killed him.
To support this I offer in evidence the fact that only a few minutes after shooting Pettigrew in the back, Dobby is more than happy to try to murder another one of Harry's enemies (Bellatrix) by dropping a three-tonne chandelier on their head. He clearly has no compunction about killing people in order to protect his friend Harry, despite his rather feeble protestations that he only meant to injure or maim.