Bale hobbled off in the second half of the London derby after falling awkwardly following a shot at goal.
Spurs fans feared their star winger could be set for a long-term lay-off, but Villas-Boas played down those concerns after the match.
The Tottenham manager also lost Michael Dawson during the game due to a hamstring injury, but he could be fit for next weekend's game at Everton.
"Both Bale and Dawson have suffered hamstring muscle injuries," Spurs boss Andre Villas-Boas said in his post-match press conference.
"One looks more serious than the other although both are controllable.
"With muscle injuries it's very difficult but it might keep him out for one to weeks. Dawson a little bit less."