The revival of the play is set in a Pittsburgh boarding house in 1911. It is currently nominated for six Tony Awards.
Three theater executives, who wished not to be identified by name, confirmed the famous couple's Saturday night plans to The New York Times, but cautioned their schedule could change.
"The president and the first lady will be making a personal visit to New York tomorrow," Bill Burton, a spokesman for the president, told the newspaper, without offering any additional details.
Michelle Obama was in New York recently to speak about the importance of the arts in the United States.