The 19-year-old damaged ligaments and was stretchered off during the closing stages of Saturday's 1-1 draw at Ipswich.
He is definitely out of the midweek clash and Saturday's visit of Cardiff.
Jamie Devitt is a likely replacement for Stewart, but Tigers manager Nigel Pearson has no other new injury or suspension problems and is unlikely to make any other changes.
Striker Jay Simpson will hope he has done enough to force his way back into the starting line-up after stepping off the substitutes' bench to head a late equaliser at Portman Road.
Jack Hobbs, on loan from Leicester, James Harper and Tom Cairney are all hoping to feature.