James Whittemore was taken into custody by authorities on Sunday morning after using a metal bar to pry open the entrance to the Ed Sullivan Theater, CBS News reports.
An apparently intoxicated Whittemore is believed to have smashed glass on the building's sliding doors and caused $2,000 (£1,253) worth of damage inside the building.
Police were quick to arrive on the scene following a 911 call and apprehended Whittemore on charges of burglary and criminal mischief.
Letterman's production company confirmed that his Late Show will tape as normal today when the host welcomes scheduled guests Emma Watson, George Lopez and Incubus.
Letterman has taped his nightly chatshow at the Ed Sullivan Theater since joining CBS in 1993.
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Watch the New York Daily News' footage of the damage caused by Whittemore's break-in below: