Tzolis was forced off after just 18 minutes of action in Thessaloniki after flagging up a hamstring problem to the Greek medical team.
After initially appearing to be unwilling to come off, Tzolis was eventually replaced by Georgios Masouras, and the hosts went onto let a two-goal lead slip away as the Netherlands claimed a 2-2 draw.
Greece head coach Ivan Jovanovic confirmed he will go for tests later today, but he's unlikely to feature in their final game of the international window, at home to Germany on October 4th.
"How am I supposed to handle it? I’m his coach, I tell him to come off and he tells me: ‘I’m not coming off.’ What am I supposed to do?"
Arteta has already seen Declan Rice and Kai Havertz pick up injuries on international duty as the Gunners return to action at home to Leeds United on October 10th.