The Spanish midfielder rolled his ankle when attempting a cross in the opening stages of Monday's 2-1 home defeat to Wigan.
The former Everton man received treatment off the pitch - during which time Wigan scored their second goal - but he could not continue.
Scans have since revealed no break but the ligament damage is serious enough to keep the 30-year-old out for the rest of the campaign.
The news is a big blow for Arsenal as Arteta has become a key figure this season since his £10million move from Merseyside on deadline day last August.
It also leaves Gunners boss Arsene Wenger with a midfield selection headache as he prepares his side for this weekend's game with Chelsea.
The Frenchman is also without Jack Wilshere, who will not play again this campaign, while Abou Diaby is not yet match fit.
With Yossi Benayoun unable to play against his parent club, Welsh midfielder Aaron Ramsey is the most likely senior option to come in for Arteta.
Arsenal are currently in third place in the Premier League, five points ahead of north London rivals Tottenham who have a game in hand.
After Saturday's clash with Chelsea at the Emirates Wenger's men face trips to Stoke and West Brom and a home match with Norwich in their remaining fixtures.