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.
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