The 28-year-old forward was forced off with a suspected ankle injury after scoring in his side's 2-0 win over Genoa, with Mario Balotelli replacing him after just 22 minutes.
The striker is set for a scan to determine the full extent of the damage, but he will take no part in next week's last 16 second-leg clash with the Blaugrana, having been omitted from Massimiliano Allegri's 22-man squad for the trip to Spain.
The news will come as a bitter blow to the Italian giants, with Balotelli ineligible to feature in the match as a result of him being cup-tied to Manchester City. Stephan El Shaarawy and M'Baye Niang are the only recognized first-team forwards available for selection for the Italian side, which carries a 2-0 aggregate edge over the Catalan giant into the final leg.
Pazzini has enjoyed an excellent run of form in recent weeks after a difficult start to his Milan career following his move from Inter, having scored six times in six victories for the Rossoneri in 2013.