The production, which will take place April 8-May 1, 2016, is separate from the national tour of the Broadway production that launches this fall.
Several other regional theatres are expected to also announce plans to stage original productions of Bridges in the coming months.
The musical ended its Broadway run May 18, 2014, after 137 performances. Despite its brief run, The Bridges of Madison County earned two 2014 Tony Awards, for Best Score and Best Orchestrations.
The romantic musical centers on a brief, four-day love affair between a National Geographic photographer and an Italian-American housewife in 1965 Iowa. Clint Eastwood and Meryl Streep starred in the 1995 film adaptation. The stage production and film were based on the best-selling Robert James Waller novel.
American Theatre Magazine first reported news of Arkansas Rep's season, which will also include the world premiere of Scooter Pietsch's workplace comedy Windfall, to be directed by Tony Award winner and "Seinfeld" star Jason Alexander. It centers on a group of co-workers who hope to win the lottery and leave office life behind.
Titles also planned at Arkansas Rep include The Little Mermaid, The 25th Annual Putnam County Spelling Bee, Peter and the Starcatcher and Macbeth.