Martinelli injured his left knee in training last month and Arsenal confirmed on Thursday that the Brazilian will not return until well into the 2021/21 campaign.
The 19-year-old had scored 10 goals in 26 appearances this term to establish himself as an important member of Arsenal's squad in his first season with the club.
"Martinelli currently recovering in a knee brace after his operation, which took place during the last week of June," a statement on Arsenal's website said.
"Surgery was successful, with consultants and our medical team very encouraged with Gabi's current progress at this stage of his recovery. He will continue his recovery throughout the close season, with the aim of a return to full training by the end of 2020."
Arsenal defender Pablo Mari is expected to return to training in September after spraining ankle ligaments at Manchester City last month.