McDonagh's play, which debuted in 1996 at the National Theatre in London, has been extensively performed in the U.S. and England. The drama bowed at the Public Theater in New York in 1998 and had its Los Angeles premiere the same year at the Geffen Playhouse.
Radcliffe plays one of the inhabitants of a rural Irish village who are fascinated by the shooting of a Robert Flaherty documentary movie nearby. His character, the "cripple" Billy Claven, attempts to land a part in the film.
The "Harry Potter" actor has previously appeared on Broadway in the 2008 revival of "Equus" and the 2011 production of "How to Succeed in Business Without Really Trying." "Inishmaan" is scheduled to run through July 20.
The staging is among Grandage's first as part of the theater company he created following his tenure at the Donmar Warehouse.
Ben Brantley of the New York Times concluded that Radcliffe "is entirely convincing as the boy who is regarded as least likely to succeed at pretty much anything in his God-forsaken rural Irish town." The production makes a convincing case that this is "one of Mr. McDonagh's most substantive plays."
Marilyn Stasio of Variety described Radcliffe's performance as "warm, sympathetic" as well as realistic for portraying his character's physical infirmities. Grandage's direction is able to balance the "sheer hilarity of the comic situation and the aching poignancy of the characters."
Newsday's Linda Winer wrote that the play is "subtler than McDonagh's more melodramatic hit gore-fests." As Billy, Radcliffe "is again wonderful, a low-key company player."
[For the record: April 21, 3:08 p.m.: An earlier version of this post misspelled the last name of Newsday theater critic Linda Winer as Winter.]