McKean has been forced to pull out of the Tony Award-nominated Broadway revival of Gore Vidal's The Best Man indefinitely after breaking his leg in the New York street accident on Tuesday (22May12).
Lecesne, who wrote Oscar-winning short film Trevor, will replace him onstage as Dick Jensen.
The actor previously portrayed a Washington Post reporter in the play, alongside injured McKean, in his Broadway debut.
Producer Jeffrey Richards tells BroadwayWorld.com, "I have worked with Michael on three previous productions... and he has never missed a performance, and I understand from his team that he has never missed a performance in his career. So this is the kind of first we are reluctant to announce.
"He is currently in stable condition, he has a broken leg."
Richards suggests McKean will not return to the show, adding, "I look forward to working with Michael again on a future project."