Rice was not included in the Arsenal squad that traveled to Italy for their Champions League match against Inter Milan on Wednesday night.
Speaking at his pre-match news conference, Arteta - who confirmed Bukayo Saka will captain Arsenal at San Siro - said: "Declan unfortunately picked up an injury against Newcastle. It is a knock, a problem on his foot, and he wasn't comfortable to put his boots on so at the moment he is not fit.
"He wasn't feeling good the last few days. We'll have to assess him on Thursday and see if he's ready for Chelsea."
Arsenal are looking for their third victory of the competition when they play Inter having won two and drawn one in the competition so far. Arteta's side then visit Chelsea on Sunday, live on .
TrendingClub skipper Martin Odegaard could hand Arsenal a major boost by making his comeback against Inter, although confirmation of Saka's captaincy suggests any appearance would be from the bench.
Odegaard - who has been out of action since September with an ankle injury - trained alongside his team-mates at Arsenal's London Colney base on Tuesday morning, and travelled with the squad to Milan.
Arteta said: "It's great to have him back. He trained with us for the first time today. He's back a bit earlier than expected, but it's great to have him here and we will decide if we use him tomorrow."
Arsenal captain Odegaard has missed his side's last 12 matches following an injury he sustained on international duty with Norway.
And although it is uncertain how many minutes he might be afforded against the Italian champions, his imminent return comes at the perfect time for the Gunners who have slipped seven points behind Liverpool in the race for the Premier League title.
Arteta said the inspirational Saka has earned the right to wear the armband on Wednesday night.
"People admire him, people respect him, they want to be next to him," Arteta said.
"He has a particular way of smiling. He's one of our leaders right now. He's one of our biggest players and one of our biggest talents. He's earned that status in the team right now."
Inter Milan boss Simone Inzaghi says retaining possession will be key if his side are to beat an Arsenal team who have been formidable in this competition so far this season.
"We are facing one of the best teams in Europe, very recognisable with a great coach," Inzaghi said.
"If you see Arsenal among 100 teams, without knowing the name, you recognise them. They played for the last two English titles point for point with Manchester City.
"We will have to try to keep the ball as much as possible, we know that we are facing a team that put on a lot of offensive pressure. We know that it will be a problem for us when they have the ball but the opposite is also true."