Local police stopped the pair - a woman aged 60 and a 17-year-old boy - on Easter Sunday at the Fountain of the Two Seas.
The monument is located in the central Piazza Venezia, close to the Colosseum and Roman Forum.
The tourists had been sitting on the side of the fountain, their legs submerged "up to their knees" in order to cool off from the spring heat, city authorities said.
"When asked for ID, the two tourists were surprised, convinced that a 'footbath' was allowed," the city hall said in a statement. "The woman, very annoyed by the steep penalty, said that she would protest at the Danish Embassy."
The arrest came after an Italian was arrested for taking a nude swim in the iconic Trevi fountain on Wednesday, where police presence has been stepped up and fines for trespassing increased following a 2 million euro restoration of the landmark.
Since January, there have already been ten violations of rules preventing trespassing in Italy's fountains, following 48 such crimes last year.
Security in the capital was beefed up over the Easter weekend, with extra officers stationed at Rome's ports, train stations, and airports as well as at popular tourist sites ahead of the holiday.