Matt Prior was ruled out of England's tour match against the Australian Invitational XI this week with a calf problem but England remain optimistic that he will be fit in time for the first Test which starts in Brisbane on November 21.
But, if Prior does not recover in time, Bairstow will take his place.
Vaughan, who led England to their 2005 Ashes win, told BBC Radio 5 Live: "Jonny Bairstow will be fine batting at number seven but I would worry immensely if he has to keep in a Test match.
"I wouldn't put him in the top five keepers in England."
The 24-year-old has played 12 Test matches for England but has not kept the wicket, and has played at wicketkeeper in just one Twenty20 international for his county and has mainly been used as a specialist batsman.
And Vaughan, who played 82 Tests for England, added: "I questioned it as soon as the squad was selected.
"I just don't think he's done enough of it to withstand the pressure of an Ashes series keeping wicket.
"Bairstow is a package that could work in 20-over and 50-over cricket, but in five-day cricket, yes you need someone who can bat, but also to take those important catches.
"He hasn't done enough for Yorkshire this summer because he has been playing for England.
"He may have to keep in the hottest of pressure zones, the Gabba, in front of 40,000 spectators. The selectors feel Bairstow is the next best, but I would question that."
Prior has played 57 consecutive Test matches - 72 in total - for England since making his debut in 2007 and the 31-year-old has claimed 220 Test match victims.
And Vaughan expressed his concern if the Sussex man is not fit to return in Brisbane.
He added: "The injury to Matthew Prior is a massive, massive concern.
"He's been brilliant for England for three or four years and is the engine of the team.
"Prior is a confidence player, he really likes to be in the middle, scoring runs. He could go into that first Test without any cricket."