DAVID Letterman’s eye infection forced him to miss last night’s “Late Show.”

Letterman, who talked about the infection on Tuesday’s show, was replaced by Bruce Willis, who was scheduled to be a guest on last night’s show along with Dan Rather and Grammy winner John Mayer.

“Dave has an infection of his right eye. It’s under treatment and we expect a full recovery,” said Dr. Louis J. Aronne.

Repeats of “Late Show” will air tonight and tomorrow (11:35 p.m./Ch. 2). The show is on vacation next week.

Last night marked the only time Letterman ever missed a show, barring his five-week recovery from emergency bypass heart surgery in early 2000.