Martinelli was on the receiving end of a heavy tackle during Arsenal’s 3-0 loss to Brighton last Sunday and had to be substituted after 20 minutes.
The forward left Emirates Stadium wearing a protective boot and underwent a scan at the start of this week.
Martinelli has suffered ankle ligament damage and is now set to miss Arsenal’s trip to Nottingham Forest on Saturday, as well as their final game of the season at home to Wolves next week.
The Brazilian, however, is expected to be back in time for the start of pre-season in July, provided there are no setbacks during his recovery.
Brighton midfielder Moises Caicedo, who made the tackle on Martinelli, apologised on social media after.
“If I could turn back time I wouldn’t have made that bad tackle,” he tweeted.
The Gunners are currently second in the Premier League and their hopes of beating Manchester City to the title are all but over.
City will win the title if Arsenal fail to beat Forest on Saturday and, even if the Gunners win, Pep Guardiola’s side will be crowned champions with a victory over Chelsea on Sunday.