The Athletics pitcher is to appear on Tuesday's edition of the talk show.
Braden led the A's to a 4-0 victory over the Tampa Bay Rays Sunday.
He will be the sixth pitcher to visit the "Late Show" after throwing a perfect game. Hurlers Kenny Rogers, David Wells, David Cone, Randy Johnson and Buehrle all visited the CBS broadcast after their historic pitching performances.
Also dropping by the "Late Show" Tuesday will be actress Queen Latifah, actor and comedian Will Forte and musical guests MGMT, CBS said.