The Welshman sustained the injury while racing onto a Jan Vertonghen pass and shooting straight at Mark Schwarzer during an otherwise convincing second-half performance from Spurs.
Spurs boss Andre Villas-Boas confirmed that Bale, who was replaced by Gylfi Sigurdsson during the second half at Craven Cottage, will be out of first-team action for at least a week due to the injury.
Michael Dawson also picked up a knock to his hamstring as Tottenham picked up its third consecutive win, but Villas-Boas insists the defender's injury is not as serious as Bale's.
Neither are expected to feature in Spurs' midweek Europa League clash with Panathinaikos, but Bale now faces a race against time to be fit for the visit of Everton to White Hart Lane on Dec. 9.
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