The actor was taken to hospital in critical condition after the accident in Manhattan's Upper West Side, the New York Daily News reports.
McKean's condition was later upgraded to stable but he has suffered from a broken leg, his publicist Harriet Sternberg said.
"He'll be okay," Sternberg said. "Hopefully, he'll be fine. It's pretty devastating."
Two other people were also taken to hospital after the incident, but officials have said that the extent of their injuries was unknown.
McKean's wife Annette O'Toole has flown in from Los Angeles to be with her husband, who will now miss his performance in the Broadway production of The Best Man tonight.
"It's the first time he will have ever missed a curtain in his entire life," Sternberg said. "His understudy has never gone on in 40-plus years."
McKean also starred in the television show Laverne & Shirley, appeared in several episodes of Saturday Night Live, and has starred in movies such as Planes, Trains & Automobiles, Coneheads, Little Nicky, Best In Show and For Your Consideration. He also recently had guest roles in Happy Endings and Homeland.