The England international has been struggling to regain full fitness following groin and stomach surgery.
He had been forced to sit out England's final two 2014 World Cup qualifiers as a result, and will now miss crucial contests at club level.
Arsene Wenger expects Walcott to be absent from his plans for a Champions League clash with Borussia Dortmund, a Premier League fixture with Crystal Palace and a Capital One Cup tie with Chelsea.
He said: "He had a setback on Thursday. He had to stop, to jog again.
"I don't think we will see him against Dortmund, nor Crystal Palace, nor Chelsea.
"He is at least two weeks away now."
Walcott now faces a battle to regain his place in the Arsenal side, as they continue to top the Premier League table, and a race against time to prove his fitness ahead of England's friendly dates with Chile and Germany in November.