McGregor sustained the injury in a first-half collision with West Ham midfielder Mohamed Diame that saw him sent off and allowed Mark Noble to put the hosts ahead from the penalty spot.
The Scotland international received medical treatment on the pitch before being gingerly helped from the field and Bruce said that he would spend a night in hospital to have the damage assessed.
"McGregor is in a bad way - kidney damage," the Hull manager said in his post-match press conference. "A specialist is on his way to see him. It is a contusion on his kidney. We're hoping it's not ruptured. He's gone to hospital and he'll be staying overnight."