We don't know. We know very little about Vercingetorix's family--his father was Celtillus, an Avernian noble who, Caesar says, aimed at the kingship of all Gaul and was put to death for it. It's not entirely clear what Caesar means by this. What he says is:

cuius pater principatum Galliae totius obtinuerat et ob eam causam, quod regnum appetebat, ab civitate erat interfectus

whose father had obtained the chieftainship of all Gaul and towards this end, because he sought kingship, was put to death by his state

That's more than a bit unclear, made moreso by the fact that Caesar has to sort of make up terms to correspond to Gallic political words that Latin does not have. Celtillus apparently held some high chieftainship or some kind of high position within some kind of unified Gallic counsel--principatus isn't exactly clear. It's derived from the word that the Romans used to describe the most notable men in the state (politically it has the specific meaning of those who get to address the senate first, usually the consulars from the year before, followed by other former magistrates), and Caesar uses it to refer to Gallic leaders in general. So it's confusing what sort of a position Celtillus held exactly, especially since there's little evidence to suggest a unified Gallic chieftainship before Vercingetorix. Also confusing is what Caesar means by ob eam causam, "towards this cause." Obviously this means that Celtillus was killed for his attempts at increasing his power, but it could technically place the causality of his death on his chieftainship in general or more specifically on his attempt to turn Gaul into a kingdom. Plutarch mentions Vercingetorix's (whom he calls Οὐεργεντόριξ) father as being put to death for τυραννίδα δοκοῦντα πράττειν, "plotting at tyranny," whatever that means exactly.

Vercingetorix only has one other known relative, his uncle Gobannitio, whom Caesar mentions as among those who exiled him from Gergovia when he proposed to join the rebellion of the Carnutes. Vercingetorix's exact age is unknown, but he was very young--Caesar refers to him as an adulescens--and it's unlikely that he had any children. Not even the name of a wife or father-in-law is known, so it's not even known if he was married (which I think is somewhat unlikely, since surely his wife would've been mentioned at Caesar's triumph--Arminius' wife and family feature rather prominently in the dealings of that affair, for example). In all likelihood Vercingetorix's line died with him during Caesar's triumph in 46