The Grammy Award-winning singer is expected to appear in the finale of the June 23 performance.
"Etheridge, whose latest album 'Fearless Love' recently was released on Island Records to widespread acclaim, will be making her Broadway debut on the stage of the Nederlander Theatre with this performance that will feature a new song, not already in the show, that will be pulled from the canon of rock 'n' roll's iconic songs," the musical's producers said in a news release.
Etheridge is also scheduled to perform a full-length concert in New York July 14 at The United Palace Theatre.
"Million Dollar Quartet" has been nominated for three Tony Awards -- best musical, best performance by a featured actor in a musical for Levi Kreis and best book of a musical for Colin Escott and Floyd Mutrux.
The show is about the historic, one-time jam session of Johnny Cash, Jerry Lee Lewis, Carl Perkins and Elvis Presley in 1956.