The Swede, who scored both goals in Barca's 2-2 Champions League quarter-final first leg draw at The Emirates stadium on Wednesday, pulled out of the starting XI during the warm-up for the La Liga match against Athletic Bilbao at the Nou Camp.
An initial examination revealed he had a small tear in his right calf.
Earlier, Barca coach Pep Guardiola told a news conference: "...it will be difficult for him (Ibrahimovic) to play (against Arsenal). I hope he'll be ready at least for the Madrid game. He had complained of some problems after the match in London."
The European champions face a busy week with Arsenal visiting on Tuesday before Barca visit La Liga title rivals Real Madrid for 'El Clasico' at the Bernabeu next Saturday.
Ibrahimovic was replaced by Bojan Krkic before kickoff against Bilbao and the youngster scored twice in a 4-1 victory.
Defender Gerard Pique also finished the game with a muscle problem and will be out for six to seven days, the club added.
The Spanish international is suspended for the Arsenal game but could make it back in time for the visit to Real.
