Nothing explicitly prevents it. It doesn't really matter anyhow; Congress has the exclusive power to impeach. Impeachment is the mechanism the constitution provides deal with criminal presidents and the president can't block it.
Make no mistake; the last thing Comey and Clinton+Obama et al. wanted was to fill news cycles with "FBI investigation reopened" 11 days out. It's bad, whatever it is, and this is a CYA move; Comey believes he needs to be able to claim he notified Oversight and made this public prior to the election.
That would be like Democrats impeaching Bush and getting Cheney instead.