The ceremony will be held at the Staples Center in Los Angeles, but the Hamilton performance will be piped in via satellite from the stage of the Richard Rodgers Theatre on Broadway.
Creator and star Lin-Manuel Miranda was quoted as saying, "We're going to do the opening number, scream with joy, and then celebrate the fact that we were just on the Grammys. Best night ever."
Hamilton is nominated for Best Musical Theatre album.
The musical is usually dark on Monday nights, but an audience will be invited in that night for the special performance.
Watch a video the cast made to announce the Grammy gig:
Good morning guys.
We will see you on the Grammys live! Gulp! https://t.co/tuMVQmPFoT