Tottenham confirm goalkeeper Lloris faces up to seven weeks out
The former France international, who captains Spurs, suffered the injury in Sunday's 1-0 win against Premier League champions Manchester City.
Fraser Forster will now step up to the number one position as north London club Spurs, fifth in the Premier League, enter a pivotal part of the season.
Tottenham visit Leicester on Saturday before resuming their Champions League campaign against AC Milan next week.
Stellini spoke to the press on Thursday in the absence of Antonio Conte, who was pictured on the training ground after returning from gallbladder surgery.
"We are all disappointed about Hugo and his injury but we have a good, experienced goalkeeper in Fraser Forster with a great experience in the Premier League and good experience in the Champions League," he said.
"We have a tough five weeks in front of us. We trust in Fraser so we are happy to play with him in the squad and also we say to Hugo 'see you soon'. He needs a good recovery, maybe between five and seven weeks to be back with us."
Forster, who signed from Southampton on a free transfer last year, has played just four times for Spurs so far and has made only one Premier League appearance, in the 2-2 draw with Brentford on December 26.
Lloris, 36, retired from international football following the recent World Cup in Qatar.