McKean, 64, is starring on Broadway in the revival of "The Best Man." He is also known for his work in the films "This is Spinal Tap," "Best in Show," "A Mighty Wind" and For Your Consideration," as well as TV's "Laverne and Shirley."
The New York Daily News said McKean was seen bleeding from the head after a car knocked him down just before 3 p.m. EDT.
"He'll be OK. Hopefully, he'll be fine," his publicist, Harriet Sternberg, told the newspaper. "It's pretty devastating."
Sternberg said McKean's wife, actress Annette O'Toole, was flying from Los Angeles to be with her husband.
"It's the first time he will have ever missed a curtain in his entire life," Sternberg said, referring to McKean's being unable to perform in the play. "He's never missed stage, screens in film or television. His understudy has never gone on in 40-plus years."
McKean and O'Toole were nominated for an Original Song Oscar in 2003 for "A Kiss at the End of the Rainbow" from "A Mighty Wind."
The Daily News said no arrests were made in the incident.