Levine, the Met's music director recently canceled all of his appearances for the remainder of the season after injuring his shoulder. Paul Nadler was previously named to replace him in a production of Beethoven's Fidelio that opens March 20.
Benini will lead most of the run of Don Pasquale, including the premiere of Otto Schenk's production on March 31. Inouye will lead the last two performances on April 25 and 28.
Anna Netrebko and Juan Diego Fl‹rez star as Norina and Ernesto.
Benini has conducted at La Scala, the Lyric Opera of Chicago, and the Paris Opera, as well as the Met. Inouye, a former assistant conductor at the Met, appeared at the company's outdoor summer performances last summer.
Replacement conductors have not yet been named for the Wagner's Lohengrin, which runs April 17-May 6, and Parsifal, which runs May 12-18.