McKean, 64, was forced to drop out of the play late last month when he was hit by a car while walking in New York and broke his leg.
Blum will start playing the role of Dick Jensen Tuesday. He previously played the character in the 2000 Broadway revival of the show. The current revival is to run until Sept. 9.
Blum appeared off-Broadway this past year in Paul Weitz's "Lonely, I'm Not" at Second Stage and "We Live Here" by Zoe Kazan at Manhattan Theatre Club. Perhaps best known for his work in the movies "Desperately Seeking Susan" and "Crocodile Dundee," he also appeared on Broadway in "Twelve Angry Men," "The Graduate," "A Thousand Clowns," "Lost in Yonkers," "My Thing of Love" and "The Merchant."