"Girl from the North Country" features the songs of Bob Dylan and is set in Depression-era Minnesota.
Unlike many other Broadway shows, "Girl from the North Country" has not had to cancel any performances since reopening in October, but box office revenue is down.
"It's very sad news, and at the moment, there are just not the audiences on Broadway for our show," producer Tristan Baker said. "Running a show on Broadway is a challenge in the best of circumstances. It's a very tough thing to do anyway."
There are plans to reopen the musical at another theater sometime in the spring.
The show's final performance at the Belasco Theatre is Jan. 23.
The play "To Kill A Mockingbird" has announced plans to move into the Belasco in June.
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