The man, 24, carved a “name of a city” into the handrail on Monday, City of London Police said, and that section of the railing may need to be replaced.
He was spotted on CCTV by Tower Bridge security staff and arrested in connection with criminal damage and possession of a knife.
The man has been bailed pending further investigations.
Tower Bridge, London’s most famous bridge, attracts close to 500,000 tourists every year.
The incident comes just months after a gym instructor who lives in England carved his and his girlfriend’s names into the side of the Colosseum in Rome with a key.
Ivan Dimitrov was filmed engraving a message reading “Ivan+Hayley 23” on the Colosseum on the afternoon of June 30.
Italian Culture minister Gennaro Sangiuliano called the writing - carved into the almost 2,000-year-old Flavian Ampitheatrewhich attracts six million people to the Italian capital every year - a “serious, undignified and a sign of great incivility”.
Mr Dimitrov penned an apology in which he expressed his “profound embarassment” and said he only learned of the Colosseum’s “antiquity” after vandalising it.