The 32-year-old was sent off midway through the first half at Upton Park after bundling into West Ham midfielder Mo Diame to concede a penalty.
McGregor had received treatment on the field immediately after the challenge and Bruce confirmed after the game that there are worries over the damaged caused.
"McGregor is in a bad way, kidney damage," the Hull boss 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."
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