James Whittemore, 22, of Manhattan was arrested in the lobby of the theater, located on Broadway between 53rd and 54th streets, at about 7 a.m. and charged with burglary and criminal mischief, police said.
He was being held pending a court appearance later on Sunday.
The theater, where Letterman tapes CBS' "Late Show." was closed at the time. Whittemore was arrested after police received a 911 call.
The historic theater was home to "The Ed Sullivan Show," which featured such memorable appearances as the Beatles in 1964.
Letterman has been a more direct crime victim, notably when Margaret Mary Ray was arrested and charged several times for trespassing and stalking the talk show host starting in the late 1980s.
Read more: Yahoo