PSG loses in French Cup quarterfinals
Evian scored all three of its penalties to win 3-1 in the shootout after the match ended 1-1 to progress to the semifinals.
Ibrahimovic's spot kick was saved by Bertrand Laquait, while Thiago Silva struck the crossbar. PSG forward Ezequiel Lavezzi scored with his penalty but Cedric Barbosa converted Evian's winner.
PSG's hopes of winning the double are over, although the big-spending club is still on course for the French league title. Evian is three points above the relegation zone.
Javier Pastore gave PSG an eighth-minute lead, but Evian leveled in the 43rd when an unmarked Saber Khelifa prodded in from close range after a counterattack.
PSG midfielder Thiago Motta was sent off two minutes from the end of extra time for a foul on Barbosa.
Bordeaux is also through after winning 3-2 at second-division club Lens. The topflight club was behind for nearly 50 minutes after goalkeeper Cedric Carrasso's own goal.
But Gregory Sertic leveled and Cheick Diabate scored late double. Zakarya Bergdich pulled one back for Lens in stoppage time.
Bordeaux midfielder Ludovic Obraniak had a spot kick saved.