The backpackers, a man and a woman in their 30s, were arrested by local police after a resident spotted them sitting on the steps using a camping stove.
City officials said the German pair from Berlin offended “the rules of public decorum and respect”.
Photographs issued by the city showed the two tourists sat with their bags on canal steps at the foot of the bridge before the arrival of police on Friday morning.
The male tourist was fined €650 (£584) and the woman was fined €300 (£270).
Both tourists were issued with a “Daspo” behaviour order – similar to that used against football supporters – and asked to leave the city.
The laws public decorum laws were introduced after residents complained about the bad behaviour of tourists at the Unesco world heritage site, including picnicking, diving into canals, washing in fountains or walking around bare-chested or in bikinis.
“Venice must be respected and those rude who think they come to the city and do what they want must understand that, thanks to the girls and boys of the local police, they will be taken, sanctioned and removed,” said Luigi Brugnaro, the mayor.
“From now on furthermore, we will also report them to the embassies and consulates of their countries of origin.
“Our city will always be open and welcoming to all those who want to come and visit it, at the same time we will be intransigent with those who think they will come and do what they want.”