An American in Paris,” the stage musical that meshed Broadway and ballet, will close on Broadway in January — but the major renovations planned for the production’s venue, the Palace Theater, won’t necessarily begin immediately after its exit.

The well-received musical, which gave “Fun Home” a run for its money in the competition for the 2015 Tony Awards, launched strong at the box office, with weekly sales regularly topping $1 million all the way through 2015. More recently, however, receipts have tapered faster than many would have expected, prompting observers to note that the show, a new musical based on the 1951 Vicente Minnelli movie and its well-known Gershwin score, seems to be behaving at the box office less like a new musical and more like a revival (a category that tends to have a shorter Broadway shelf life). Last week “An American in Paris” brought in just under $700,000.

The production hasn’t yet recouped its $11.5 million capitalization, but producers — led by Stuart Oken, Van Kaplan and Roy Furman — said they expect the show to tip over into the black before the Broadway staging finishes. The title is already on tap to kick off a national tour in Boston in October, while a London production is lined up for March 2017 with a cast led by its original stars, Robert Fairchild and Leanne Cope.

Meanwhile, the Palace Theater, the venue where “American in Paris” opened in March 2015, is scheduled to undergo a massive construction and renovation project that will lift the landmark theater some 30 feet higher within the building that houses it, thereby yielding four floors of valuable retail space on the ground floor and basement levels. It’s a project that will take one of Broadway’s most substantial musical houses out of commission for about three years.

However, it won’t necessarily happen immediately after the closing of “American in Paris.” According to sources familiar with the plans as they stand right now, there’s a decent chance that another show will slot into the Palace before the renovation process begins — although probably not one aiming for an extended, open-ended run.

“An American in Paris” won four 2015 Tonys, including the choreography award for director-choreographer Christopher Wheeldon. The show will close at the Palace Jan. 1, after 719 performances and 29 previews.