Mayor Luigi Brugnaro posted a video on social media showing a pair of surfers heading down the famed waterway as the sun rose in the distance.
The mayor asked for help in apprehending what he called “two overbearing imbeciles who are making a mockery of the city” and promised dinner for anyone who identified the scofflaws.
“I ask everyone to help us identify to punish them, even if our weapons are really blunt — We urgently need more powers for mayors in terms of public safety,” he said.
In a later post, he said their boards had been confiscated and that the two would soon be apprehended.
He did not specify what punishment they faced, but the city has a long list of rules governing the behaviour of visitors.
Venice has long suffered over-tourism, and with it lapses in decorum by visitors.
The city fined two German travellers €950 (about $1400) in 2019 for making coffee on the 430-year-old Rialto Bridge.
Visitors also are prohibited from swimming in the canals and from eating on the steps of monuments.
From next year, day-trippers will have to pay a visitor’s tax to help offset the elevated costs of providing services in the canal city.