The 42-year-old was using a sharp-edged stone to engrave a large K, some 25 centimetres (10 inches) tall, onto the brick surface, the Italian ANSA news agency said.
The judge also handed down a suspended four-month jail sentence.
He was the fifth visitor to the Colosseum to be penalised for defacing the famous monument this year.
The others were an Australian father and son, and two teenagers, from Canada and Brazil.
The Roman daily Il Messaggero said authorities would increase the number of surveillance cameras and step up visual and audio warnings against vandalism.
The Colosseum, the biggest amphitheatre built during the Roman Empire standing 48.5 metres (159 feet) tall, welcomes more than six million visitors a year.
Long-delayed repairs to the 2,000-year-old monument, once used for bloody gladiatorial contests, began in September. Funded by Italian billionaire Diego Della Valle,the refurbishment is expected to end in 2016.