Allen has used the one-act format before, having collaborated with May and David Mamet for "Death Defying Acts" in 1995.
The new mini plays, titled "Relatively Speaking," will be directed by John Turturro, who has appeared in several films by Coen and his brother Joel.
Producers said previews will begin in September with an opening in October. Decisions regarding casting and location will be made later.
Allen is returning to the New York stage as a playwright following the off-Broadway productions of his "Writer's Block" in 2003 and "A Second Hand Memory" in 2004.
The Associated Press contributed to this report.