Bale had to be stretchered off towards the end of Tottenham's 2-2 Europa League draw with Basel at White Hart Lane and Spurs fans feared his superb campaign might be set to end prematurely.
But Villas-Boas said: "He rolled on his ankle and, at the moment, there is a lot of pain, but hopefully it is not as bad as it could have been.
"We still need to get assessment that we can only have on Friday."
Bale picked up the injury in stoppage time towards the end of a thrilling tie, going over on his ankle when he challenged for the ball and staying down, clearly in great pain, before being carried off.
Photos of the injury showed Bale's foot bent almost at right angles to his leg but Villas-Boas added: "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 on Friday.
"There is a big, big possibility that, if we stay positive, he will be fit for the Man City game (on 21 April) and it will only take him out of 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."
Lennon and Gallas hurt
Spurs fought back from 2-0 down against a lively Basel side but also lost Aaron Lennon and William Gallas to injury.
Villas Boas said: "We still have a big squad and the ability to adapt. We just have to play against Everton (on Sunday) and see when these players get back to make us even stronger.
"Gallas may have a small tear on his calf but again it is about the assessment on Friday."