Djourou suffered the injury in a collision with team-mate Bacary Sagna in the latter stages of the 2-0 loss.
Arsenal boss Arsene Wenger said after the match: "Unfortunately we lost Johan Djourou for the rest of the season - dislocated shoulder - season over."
The Swiss centre-back, who has had loan spells at Birmingham City, missed most of the 2009 season with a knee injury.
He has made 29 appearances in all competitions for the Gunners this season.
Source: BBC Sport
Source: BBC Sport