The Welsh winger badly went over on his ankle late in Spurs' 2-2 Europa League quarter-final first leg draw with FC Basel on Thursday night, requiring a stretcher from the pitch.
However, Villas-Boas was quick to ease the fears of Tottenham supporters during the post-match press conference but did indicate that Bale would miss the weekend's clash with Everton and next Thursday's return leg with Basel.
"Gareth has rolled over his ankle. We still need to get assessment that we can only have on Friday," he said.
"It shouldn't be as bad as it looks because Gareth has torn that ligament before and there's nothing to tear now. There is lots of swelling and the pain is obviously very, very big but we hope to assess him tomorrow.
"There is a big possibility he is going to be able to make it for the Man City game and he will only miss the next two games.
"We've played without Bale before and we've got the results that we needed, results that have put us in the position we are in the league.
"We recognise the form the player is in and the squad will step up a level for his absence. Key players are always missed by any team but we have played without him before."