Villas-Boas has conceded that Defoe's injury leaves Spurs short in attack as they continue to fight on two fronts.
He told reporters at a pre-match press conference: "Jermain has a muscle injury that is going to take him out of the next two games definitely, and maybe Basel away.
"If he can't make Basel away, he should be fit [for the] week when we prepare for Manchester City. It's a big blow. It's the same muscle that he had a small tear on last month but on the other side now.
"Obviously he's a big miss because he's a player who represents a lot for us and shown tremendous quality this season."
The 30-year-old has scored 14 times in all competitions for Spurs this season.