Spurs won the north London derby 2-0 on Sunday at Tottenham Hotspur Stadium, with Harry Kane scoring the second goal on a counter-attack just before half time.
During the counter, an injured Partey limped towards the touchline with Arteta even attempting to push the midfielder back onto the pitch – only for the player to pull up again seconds later.
Arteta was unhappy after the game that Partey did not go to ground in a bid to stop play.
“The second goal, we get done on the counter. Thomas gets injured, he has to fall on the floor,” Arteta told Sky Sports.
“It was too quick. It was a four against two situation. Suddenly Thomas is coming towards us. I don't know exactly how it happened, he felt something serious and we will look at it and talk about it.
"It's another issue. It looks like he's got a similar injury in a similar area. We will have to assess him and see how it is."
Partey had been a doubt before the game with a thigh injury, having missed Arsenal’s previous two matches, but was eventually passed fit.
Arteta added that he was pleased with Arsenal’s performance on the day but said that the team’s goalscoring woes – the fourth worst in the division – must improve.
"[How do we improve?] By scoring goals, very simple,” he said.
“We need to score goals. If not, it's unsustainable. We need to put the ball in the net, urgently.
“In terms of the performance they did everything that I asked them to do. Absolutely everything. We played the way I believe we had to play this game.
“You look at the stats, they're all in our favour, but we have to put the ball in the back of the net.”