Bale, who has scored 22 goals for Spurs so far this season, was carried off on a stretcher in the dying seconds of Thursday night's 2-2 Europa League quarter-final draw against Basle.
Villas-Boas said after the game that the injury does not appear to be as worrying as original images suggested and, following a scan on Friday, the Wales international could return in time for the Barclays Premier League clash with reigning champions Manchester City on April 21.
Spurs face Everton on Sunday ahead of the return leg against Basle in Switzerland but Villas-Boas believes his side will cope without Bale.
"We have suffered setbacks before and managed to jump out of them so lets wait and see," he said.
"We've had his absence before in different moments of the season and we had people stepping up to the game."
When asked if it was a chance for other players to come in and shine, the Portuguese replied: "I think so. When an injury happens to a player who has played most of the time it another player to step in.
"We have those players - [Gylfi] Sigurdsson has gone back to his goalscoring form, scoring two during the internationals and once against Basle and [Lewis] Holtby was also at a very, very good level."
Defender William Gallas and winger Aaron Lennon were also forced off with injuries in the draw with Basle but, like Bale, Villas-Boas expects to have them both back in contention sooner rather than later.
He said: "Due to the postponement of the Chelsea game most of the players will be back soon enough to play the remaining six games."
The trio of injuries mean Villas-Boas' squad will be pushed to the limits as they search for both Europa League success and a top-four finish in the Premier League.
But the former Chelsea manager reckons he has enough quality at his disposal that he will be able to continue his policy of rotating his squad whenever possible.
"We have a very, very strong squad and as you can see we rotate quite frequently and the quality of squad allows us to that," he said.
"We will rotate at Everton and have fresh legs coming in, with injuries we have the opportunities for another couple of people.
"We have used it [rotation] a lot, you have seen us rotate goalkeepers in Europa League ties and rotate central defenders in Premier League and Europa League games.
"You try and use the fresh legs to have the squad balanced and ready for the Sunday game - you always benefit because fresh legs are as important as players who are regular starters."