The 19-year-old Brazilian was named in the Gunners’ starting lineup for the third-round tie at Emirates Stadium but was replaced by Reiss Nelson minutes before kickoff.
Martinelli returned to action in December after a prolonged absence due to a knee problem but is now set for another spell on the sidelines.
"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," boss Mikel Arteta said after the game.
"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. I imagine that we're not going to have good news with him.
"We really want to know what's going on. He's a character and he wants to play. He doesn't care and can handle pain but I don't know. Hopefully there is nothing too serious but to start with, it didn't look too good."
Emile Smith-Rowe and Pierre-Emerick Aubameyang scored in extra time to help holders Arsenal seal a spot in the fourth round and extend their winning run to four games in all competitions.
Arsenal, who are 11th in the Premier League with 23 points from 17 games, host 14th placed Crystal Palace on Thursday.
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