The Thunder are trying to close out the defending champions in a sweep.
It's not clear when the 6-foot-10, 270-pounder injured his hip and there was no early word as to how severe the injury might be. If the Mavs win Saturday, the series will shift back to Oklahoma City on Monday for Game 5.
If the Thunder close it out, they will await the winner of the Los Angeles Lakers-Denver Nuggets series.
Perkins averaged 5.0 points and 7.7 rebounds in 27.7 minutes in the first three games and was a strong defensive presence in the paint. He left Game 4 with two rebounds and two assists in 7:51.
Oklahoma City has received little production from backup center Nick Collison in the series, and Nazr Mohammed has played just five minutes of garbage time in OKC's Game 3 blowout.