Estelle Parsons as Alexandra in Arena Stage at the Mead Center for American Theater’s production of The Velocity of Autumn. (Teresa Wood)

Bolstered by the well-received performances of its stars, Estelle Parsons and Stephen Spinella, Arena Stage’s production of “The Velocity of Autumn” is moving to Broadway. The comedy-drama by Eric Coble — who, like director Molly Smith, is making a Broadway debut — is scheduled to begin performances at the Booth Theatre on April 1 and officially open April 21, lead producer Larry Kaye announced Thursday.

“I keep pinching myself, but I’m thrilled,” said the Washington-based Kaye, who has been positioning “Velocity of Autumn” for a Broadway run since seeing it in a production in Cleveland last year. He added that being able to produce the play in the highly prized, 766-seat Booth — on Shubert Alley in the heart of Times Square — was especially gratifying. “It was my top choice. It was all of our top choices,” he added.

The 95-minute play, which ran in Arena’s Kreeger Theater from Sept. 6 to Oct. 20, is set in the Brooklyn brownstone in which Parsons’s octogenarian Alexandra has barricaded herself and rigged her living room with dozens of Molotov cocktails. The premise is far-fetched, but the problem Alexandra confronts is not: Her children want to move her out of her familiar surroundings and into an old-age home. Her estranged youngest son, Spinella’s Chris, has been delegated to break in and try to coax her out.

The play received a mixed notice from The Washington Post and a slightly warmer one from the New York Times, but its stars won unanimous praise. Given the material, the play can probably expect to do well on Broadway with older audiences. But it will probably find itself competing with another new play about an aging maternal figure, Terrence McNally’s “Mothers and Sons,” starring Tyne Daly and beginning performances at the Golden Theatre on Feb. 23.

“The Velocity of Autumn” had been planned to open on Broadway this past spring, but negotiations for a theater fell through, Kaye said. So the play went instead to Arena, where Smith is artistic director, with Kaye sharing a portion of the production’s costs. The delay allowed the production to test its appeal to audiences. Executives of the Shubert Organization, which owns the Booth and 16 other Broadway theaters, traveled to Washington to see it, he said.

“Velocity” will be the third production on Broadway this season that first will have been produced in Arena’s Kreeger space. “A Time to Kill,” a stage adaptation of the John Grisham novel that received poor notices at Arena in 2011, fizzled on Broadway this fall. Performances of the more favorably reviewed “A Night With Janis Joplin,” which was presented in two runs at Arena as “One Night With Janis Joplin,” continue at Broadway’s Lyceum Theatre.

Smith said it was “a real honor” to add her name to the relatively “few” women who have had the chance to direct on Broadway.

“This is a wonderful case where we waited, and the production was strong and the perfect theater was found,” said Smith, who is directing two shows at Arena in the winter — “Mother Courage And Her Children,” with Kathleen Turner, and the world premiere of Lawrence Wright’s “Camp David” — before opening “Velocity” in New York.

Of the play’s focus on the plight of an older woman, she added: “My guess is this is the kind of story that is happening in living rooms all over America. We’re that great, big mirror back on society.”