The Spaniard should return to the Gunners first-team by the end of January, but will miss fixtures against Swansea City in the FA Cup, and Chelsea and West Ham United in the Premier League.
But the report claims he could return to the squad to face Liverpool on January 30. Goal.com report that the former-Everton midfielder suffered a small tear to his calf, which should sideline him for 'two to three weeks'.
The midfielder limped out of training on Friday, and missed the Gunners' 2-0 defeat to Premier League champions Manchester City at the Emirates Stadium on Sunday.
Initial fears that the injury was worse than expected have been eased by the test results, which reportedly showed no long-term damage.
Arteta was believed to be in extreme discomfort on Friday, and was too injured to even take part in a pre-match fitness test prior to the Manchester City game.
Abou Diaby, himself returning from injury, took the place of Arteta in the Arsenal team.
The Frenchman could continue in midfield on Wednesday, when Arsenal take on Swansea in their FA Cup third round replay. The Gunners drew 2-2 in the first match at the Liberty Stadium, with goals from Kieran Gibbs and Lukas Podolski.