The Gunners were beaten 2-0 by Manchester City at the Emirates Stadium and will now lose the Spanish midfielder for some vital fixtures in the next couple of weeks.
"He has a scan on Monday, [he will be out for] approximately three weeks. It is a strain on his calf," said Arsene Wenger.
"Of course [it is a blow]. In midfield he gives us stability, experience and tactical knowledge. We will miss that."