The Scotland international goalkeeper picked up the problem in an incident that eventually saw him sent off in the 2-1 defeat at West Ham on Saturday.
McGregor was given his marching orders for the second time this season in controversial circumstances when he upended Mohamed Diame midway through the first half, but referee Mike Dean initially saw nothing untoward.
Dean then pointed to the penalty spot three minutes later after a consultation with his assistant and McGregor was shown a straight red card when he got to his feet following lengthy treatment after he came off worse in the collision with Diame, who appeared to handle the ball before contact was made between the pair.
And manager Steve Bruce revealed on Friday that the former Rangers keeper could remain in hospital for another week.
"Allan's going to be in the High Dependency Unit for another couple of days," said Bruce. "We think he'll leave hospital in a week or so."
Veteran stopper Steve Harper is the most likely to deputise for the absent McGregor, while the club have also recalled Eldin Jakupovic, who kept seven clean sheets in 13 appearances on loan at League One side Leyton Orient.
Hull travel to Stoke City in the Premier League on Saturday.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
