The show is to air as "In Performance at the White House" Oct. 20 on PBS stations in the United States.
"There's nothing quite like the power and the passion of Broadway music," the president said.
"It's one of the few genres of music that can inspire the same passion in an 8-year-old as it can in an 80-year-old," he said. "Whether we want to admit it or not, we all have the lyrics to a few Broadway songs stuck in our head."
Obama noted that many of Broadway's biggest stars arrived in this country as poor immigrants and said that, at their best, Broadway musicals have not just served as entertainment, but also raised social consciousness, challenged stereotypes and helped shape "our opinions about race and religion, death and disease, power and politics."