Rice injured his back during the first-half of the 2-2 draw at Emirates Stadium and he had to come off at the break.
The midfielder will now be assessed by Arsenal ahead of Wednesday’s Carabao Cup game at Brentford.
And asked if there is any danger that Rice could be out for a while, Arteta said: “Hopefully not.
“We have to assess him. It’s strange that a player like him asked to come off because he was uncomfortable. Hopefully not, but let’s see.
“He had some discomfort in his back. He was telling us during the first-half that he was uncomfortable.
“When we assessed him at half time he could not continue so we had to change him.”
Rice was one of two changes by Arsenal at half-time, with Fabio Vieira also coming off for Kai Havertz - but Arteta has confirmed that was not fitness related.
“Fabio wasn’t injured,” he said. “That was a tactical decision.”
Arsenal have been hit hard by injuries this season and they will hope Rice’s back issue isn’t a serious problem.
The club are already without Gabriel Martinelli, Jurrien Timber, Leandro Trossard and Thomas Partey at the moment.
“Well it was already a test today because we missed five big players,” said Arteta. “But it’s what we have. As well it gives opportunities to the other ones. We have a game every three days and that’s the level we have to show so go for it.”
The Italian was caught in possession by James Maddison, who teed up Son Heung-min to score his second goal.
“What happened is I love him and we love him,” said Arteta, when asked about the mistake by Jorginho.
“Errors are part of football. They’re allowed to make errors because they play and we don’t play.
“For us it’s really easy, but if there is someone who is willing to help the team and do the most of it, it’s Jorgi. We are all with him.”