McKean, whose leg was broken in the incident, is currently being treated in hospital but is said to be in a stable condition.
After stars such as Jane Lynch and Joel McHale sent McKean get well wishes on Twitter, the This Is Spinal Tap star took to the social network himself to express his thanks to everyone who had helped him.
He wrote: "Lucky man: best wife, great kids, awesome docs and nurses, priceless friends; a little overwhelmed by the sweet tweets. Love all y'all."
Meanwhile, the New York Post reports that McKean joked about the accident while speaking with Jeffrey Richards, the producer of his Broadway show The Best Man.
"We always tell each other to break a leg in this business," McKean is quoted as saying. "I never thought it would happen to me this way!"
McKean previously starred in the television show Laverne & Shirley, appeared in several episodes of Saturday Night Live, and has been in movies such as Planes, Trains & Automobiles, Best in Show and For Your Consideration.