The Brazilian was a late withdrawal from Arsenal's starting XI for the third-round tie at Emirates Stadium on Saturday, which the Gunners won 2-0 after extra-time, and replaced by Reiss Nelson.
Martinelli has only recently returned from a serious knee injury sustained in June and Arteta said the teenager was in tears when providing an update on his condition after the match.
"I am gutted. I was in my office before the game and one of the coaches came in and told me that Gabi had hurt himself, that he'd twisted his ankle," Arteta said.
"I went to the medical room and he was in tears. He was in a lot of pain and we're going to have to see how he is. It didn't look good. He was in pain so I imagine that we're not going to have good news with him".