The French right-back went off hurt during the thrilling 3-3 first leg draw on Wednesday, with the return next Tuesday at the San Siro.
"Tests carried out this morning have shown that first team player Jules Kounde has a hamstring injury in his left thigh," said Barcelona in a statement.
The Catalan giants did not specify his expected absence period, but Kounde is a major doubt for the Clasico clash with Real Madrid in LaLiga on May 11th, and will be unavailable for Saturday's visit to face Real Valladolid.
Barca lead their arch-rivals by four points and are chasing a potential quadruple this season.
Eric Garcia filled in at right-back for Barca against Inter Milan in the second half at the Olympic Stadium.
Kounde, 26, has played 53 games for Barcelona this season across all competitions.