The Spanish midfielder suffered a recurrence of the injury he first sustained in December after scoring in Saturday's Premier League win over Burnley.
Arsenal are 2-1 behind in the tie after a controversial defeat by Porto at the Dragao stadium last month.
"We cannot even take a gamble because he is just not available," Wenger told a news conference on Monday.
"We are all convinced it will be a very very short time and that next weekend he has a small chance to be back for Hull.
"If it's not Hull it will be the week after."
"We want to qualify and the absence of Cesc is not any excuse at all. We have enough players, we have a strong enough squad to still get round that and we have a very good chance to qualify."
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