Partey hasn’t played since being kidnapped in the 3-0 loss to Aston Villa before the international break.
The Ghanaian was thought to have had a thigh problem – but it looks like the blow was worse than that.
Arteta admitted Partey was in desperate need of getting back on the pitch, but it would be a few more weeks before that was possible.
“He got injured very early in the game, he wanted to continue the second half,” said Arteta.
“We knew it was a major injury. He did very well and he works very hard, he wants to be available.
“I hope we can get him back soon, but this is an area we have to be careful with and we have to be protective with the player.
“I don’t think he will be with us in the next few games.”
Meanwhile, the Gunners are in 14th place in the Premier League and the pressure is starting to mount on Arteta’s shoulders after suffering three consecutive league defeats.
But the Spaniard insists he doesn’t care about his job, only to get the most out of his players.
“It’s something that the day I decided to become a coach, I know that one day I will be sacked or leave the football club,” he added.
“I don’t know if it’s the day after signing my contact, in a month, a year or six months. I never worry.
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“My only concern is to get the most out of the players, to give the club the best possible service and to get better and better.
“I know, I repeat, in this profession, one day I will be made redundant or leave but I do not know when that will happen.
When asked if he was concerned about his team’s recent poor performance, Arteta admitted: “It’s when you lose three games in a row for different reasons at home. I am really worried, I am responsible for it.