The winger picked up a muscle injury in Sunday’s win at Goodison Park, forcing him to be substituted in the 24th minute.
The Gunners had a recovery day on Monday and then trained on Tuesday in front of the media, but Martinelli was not present.
The Brazilian is now a major doubt for Arsenal’s opening Champions League game at home to PSV on Wednesday.
If Martinelli misses out, 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 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.