In an email to The New York Times, the ABC star explained why he decided to show a rerun on May 20.
"I have too much respect for Dave to do anything that would distract viewers from watching his final show. Plus, I'll probably be crying all day, which makes it hard to work."
During a recent interview with the publication, Letterman dished on his 33-year run on television and said that none of the other late-night show hosts pushed him out of the job.
"I'm 68. If I was 38, I'd probably still be wanting to do the show," he explained.
"When Jay [Leno] was on, I felt like Jay and I are contemporaries. Every time he would get a show at 11:30, he would succeed smartly. And so I thought, this is still viable—an older guy in a suit. And then he left, and I suddenly was surrounded by the Jimmys."
Letterman added, "I'll miss it, desperately."