The £105million summer signing was forced off at half-time during Sunday’s thrilling 2-2 Premier League draw with Tottenham at the Emirates Stadium.
With a crucial game at home to Manchester City coming in a fortnight, the problem is a concern for Arsenal.
Martinelli and Trossard missed out with hamstring issues, Partey is out until next month with a groin problem and Timber is sidelined for the season with a knee injury.
Trossard will also be assessed this week. Even if they recover in time, neither Rice nor Trossard are expected to feature in Wednesday’s Carabao Cup third-round tie at Brentford. Bukayo Saka is unlikely to play in that game either, so he can be rested.
Saka also looked in discomfort following a late clash with Spurs left-back Destiny Udogie, and was substituted in stoppage time of the north London derby.
Arsenal will be hoping for good news on Rice and Trossard. The Gunners lost their way against Tottenham after Rice went off, losing his control and ability to break up play, and his replacement Jorginho was caught in possession for the second Spurs equaliser.
“He had some discomfort in his back,” Arteta said of Rice.
“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.”
Emile Smith Rowe and Reiss Nelson should come into the team at Brentford, while Jakub Kiwior and Takehiro Tomiyasu are likely to start in defence.
Midfielder Mohamed Elneny, who is back after injuring his knee in January, could also get some action as he continues to work his way back to full fitness.