The news is a massive boost to the north London side because it was feared the Welshman might be facing a lengthy spell on the sidelines when he was stretchered off during stoppage-time at the end of the 2-2 Europa League draw.
But manager Andre Villas-Boas said afterwards he was hopeful the problem was not too severe and scans have now confirmed that Bale has suffered sprained ligaments and should be able to return to action fairly shortly.
Winger Aaron Lennon and defender William Gallas were also injured on Thursday night but are also expected to return to full fitness in a fortnight.
Trio responding positively
A Tottenham statement read on Friday: "The club can confirm that Gareth Bale (sprained ankle ligaments), William Gallas (calf strain) and Aaron Lennon (soft tissue contusion below the knee) all underwent scans today after being forced off with injuries last night.
"The results of these scans have indicated that all three players are expected to return to training within two weeks.
"Bale, Gallas and Lennon have all commenced their treatment today and are responding positively."
The trio are set to miss Sunday's game with Everton and the second leg against Basle next Thursday but they could be in contention for the visit of Manchester City on 21 April.
Asked about Bale's injury on Thursday night, Villas-Boas had said: "Gareth will definitely play again this season. I'm pretty confident.
"From the medical department's first analysis, everything is positive.
"It shouldn't be as bad as it looks because Gareth has torn that ligament before and there's nothing to tear now."