The Scotland international has been in hospital since he was sent off at Upton Park for bundling over Mohamed Diame in the 2-1 defeat.
Manager Steve Bruce said the player had suffered "a really nasty injury".
"I went to see him yesterday in the high dependency unit in London, in hospital, and the kid's in a lot of pain," he told reporters on Friday.
"Overnight the observations are better but he's awaiting another CT scan this morning and we hope that it will repair ... it certainly looks like he's going to miss the rest of the season, that's for sure."
Hull, who play at Stoke City on Saturday and face Sheffield United in an FA Cup semi-final at Wembley on April 13, recalled Bosnian-born Swiss international goalkeeper Eldin Jakupovic from League One (third tier) side Leyton Orient on Thursday.
Jakupovic, 29, is expected to be used as back-up for reserve goalkeeper Steve Harper.
- Sports & Recreation