The Ghanaian player was in fine form for 75 minutes before he was seen signaling to the bench that he needed to come off due to a muscle problem.
Partey was later replaced by Ainsley Maitland-Niles at Turf Moor.
“He struggled at the end. He was cramping but that will come because he’s missed a long time. He needs some fitness back,” Arsenal manager Mikel Arteta said.
Partey was making only his first start of the season following rehab from an ankle injury during pre-season.
He returned to first-team action last week against Norwich and played a part in Pierre-Emerick Aubameyang’s decisive winner.