Corluka sidelined for several weeks
The Croatia international was carried off on a stretcher after being pole-axed by a wild two-footed tackle by Milan's former Arsenal midfielder Mathieu Flamini in the second half of the last 16, first leg clash.
"Vedran will remain immobilised in a protective boot for the next four days after a scan determined that he had sprained part of his ankle joint capsule," Spurs said on their website on Thursday.
"Following a clinical examination by a foot and ankle specialist this afternoon, it has been recommended that Vedran make a gradual return to training starting next week... he should be back in full training in a few weeks."
There were initial fears that Corluka had suffered a more serious injury after a tackle Spurs manager Harry Redknapp described as "horrendous."
Tottenham's former England defender Jonathan Woodgate, who made his first appearance for 15 months when he replaced Corluka against Milan, strained a left adductor muscle and will be assessed over the next few days, the club added.
Fourth-placed Tottenham face Blackpool in the Premier League on Tuesday and Wolverhampton Wanderers at home the following weekend before the return leg against Milan on March 9.