The Late Show host plans to step down from fronting the programme in 2015, and the news came as a shock to big fan Baldwin.
The actor has now launched a drive on Twitter to persuade Letterman to stay, urging fans to petition the Tv host via the social networking website.
He writes, "Maybe it's futile, but here goes... Letterman cannot retire. Just... just.... no. Send him this: #DontGoDave."