Scans on the 22-year-old former Portsmouth centre-half's ankle revealed he had ruptured ligaments.
Webster has played 23 games for Mick McCarthy's Championship side since joining from Pompey in June.
"It is a big blow for us and for him. It's sad for all of us, but more so for Adam as he's had a great season so far," McCarthy told the club website.
Ipswich Town defender Adam Webster is expected to miss the rest of the season after injuring his ankle in training.