Lacazette was sent off midway through last week's 1-0 defeat to BATE Borisov after swinging an arm at left-back Aleksandar Filipovic. Lacazette missed Thursday's return leg at the Emirates through suspension, but UEFA's disciplinary arm decided Friday to ban Lacazette a further two matches.
The 27-year-old apologized for the incident and admitted he "should have stayed calm."
Without Lacazette, the Gunners advanced to the next round courtesy of a 3-0 win in the reverse fixture.
Manager Unai Emery will now hope Pierre-Emerick Aubameyang can score the goals to beat Rennes and preserve Arsenal's hopes of silverware.
Aubameyang has only scored twice in the Europa League this season, with both goals coming in a 4-2 win over Vorskla in September.