Boss Glenn Hoddle revealed this afternoon that the Scottish international will be missing for at least two months and more if the problem requires surgery.
A despondant Glenn broke the news after training at Spurs Lodge this afternoon. "This is what you dread, a goalkeeping injury.
"Sully was just doing routine drills with Hans (Segers) on Sunday, just caught one on the end of his thumb and it's broken his thumb.
"He's going to be out for at least two months, probably longer. In a week's time we'll know if it needs an operation and if it does, it will be longer.
"Obviously we're all hoping Sully will be able to keep it in a cast and he'll be back anywhere between four to eight weeks.
"It's the story of this club at the moment. We'll just have to get on with it."
Glenn confirmed that Lars Hirschfeld will take his place on the bench in Tuesday night's Premiership derby at Charlton.
Goalkeeper Neil Sullivan could be out for up to three months after fracturing his thumb in training.