Injured Defoe ruled out for up to three games
The England forward will sit out Thursday's Europa League quarter-final first leg at home to Basel and Sunday's Premier League clash with Everton and could also miss the return match with the Swiss side next week.
"Jermain has a muscle injury which is probably going to take him out of the next two games definitely and maybe Basel away," Villas-Boas told reporters.
"If he can't make Basel away he should be fit for Man City.
"It's a big blow. It's on the same muscle that he had a small tear last month. It's on the other side now and it's a big miss as he represents a lot for us and he will be a big miss."
Defoe, who scored twice in England's 8-0 win over San Marino last month, came on for the final half an hour of Tottenham's 2-1 win over Swansea City on Saturday.
His absence is significant for the London club who are not well-endowed with strikers. Emmanuel Adebayor is their only other recognised centre-forward.
They are involved in a three-way battle with Arsenal and Chelsea for the final two Champions League qualification places and can ill afford a slip up at home to sixth place Everton.
Tottenham are third in the table on 57 points, Chelsea are fourth on 55 and Arsenal have 53.