The winger picked up a muscle injury in Sunday’s win at Everton, forcing him to be substituted in the first half at Goodison Park.
Martinelli will definitely miss Arsenal’s Champions League Group B game at home to Dutch side PSV on Wednesday and he is also now a doubt for in-form Spurs’ Premier League visit to the Emirates Stadium on Sunday.
The Brazilian is due to undergo further tests this week, with the Gunners hoping to learn the full extent of the damage.
“He felt something in his hamstring and we need to do some further tests to assess if there is any big damage or not,” Arsenal boss Mikel Arteta told reporters on Tuesday.
“But he will be out for tomorrow’s game, for sure. It is a possibility [he could miss the north London derby], we don’t know yet.
“As I said, we need some more tests and let’s see what happens.”
With Martinelli missing out against PSV, Leandro Trossard is likely to take his place in the starting XI.
The Belgian replaced the 22-year-old on Sunday at Everton and scored the only goal of the game as Arsenal maintained their unbeaten start to the new season.
The rest of the Arsenal squad trained on Tuesday afternoon, with Mohamed Elneny one of those present.
The Egyptian, however, is still working his way back to full fitness after picking up a serious knee injury in January.
Arteta has confirmed that Elneny is in the “latter stages” of recovery and could return this month.
“He’s in a good place. It’s been a while and a significant injury. He’s in the final stages of that process,” Arteta said.