The Blues defender was making just his ninth appearance this season at Fratton Park on Tuesday night having struggled for most of the current campaign with groin and back injuries.
Paranby sustained an ankle injury which forced him to be withdrawn seven minutes into the second half of the game against Avram Grant's side.
"I'm really gutted for Stuart," Blues boss Alex McLeish has said.
"He's felt as good as he has the whole season this past couple of weeks.
"He's had problems with his back and groin and now he's got this bang on the ankle.
"I hope he recovers quickly because he's looking back to match sharpness."
