Muti, 69, who is currently music director of the Chicago Symphony Orchestra, was recognised "for his extraordinary contributions in opera and concert".
"Maestro Muti is being recognised for his extraordinary contributions in opera and concert, as well as his enormous influence in the music world both on and off the stage," the BBC quoted the jury as saying.
The conductor is the second recipient of the prize awarded by a foundation established after the death of opera singer Birgit Nilsson.
"I was deeply touched by the jury's accolade, all the more so given my profound admiration for this unique and extraordinary artist, both as an incomparable musician and as a great interpreter," Muti said in a statement.
Foundation president Rutbert Reisch said he did not believe Nilsson and Muti ever worked together, but that the two "had a lot of respect for each other's work".
He will receive the prize at a ceremony in Stockholm on October 13.