The pair picked up the injuries in the 1-0 win at White Hart Lane but manager Harry Redknapp admits it is too early to speculate about a return date for either player.
"They both have tears," Redknapp said. "It's difficult to know how long they will be out for."
Redknapp was concerned to see both players hobble off either side of Jermain Defoe's match-winning strike, and his fears have now been realised after scans confirmed the suspicions of the club's doctors.
Already shorn of injured trio Scott Parker, Ledley King and Aaron Lennon, Redknapp watched in dismay as he lost midfielder Sandro after 30 minutes and centre-back Gallas midway through the second half, while Sandro's replacement Jake Livermore was also forced off late on with a knock.
Livermore is a doubt for Saturday's FA Cup tie against Cheltenham after splitting his lip in a clash of heads with team-mate Younes Kaboul, while Gallas and Sandro look set for lengthy spells on the sidelines.
Calf tears can take months to heal and in the aftermath of Tuesday's game Redknapp said: "Sandro I think tore a calf so that will be a long one. It looks like Gallas has as well. He felt it go."
This weekend's cup tie will at least give Redknapp the opportunity to patch up the likes of Parker and Livermore ahead of next Wednesday's crucial Premier League clash with Everton.
The match, postponed from the first weekend of the season due to the riots in London, could see Spurs draw level on 45 points with second-placed Manchester United and pull to within three points of leaders Manchester City.