Seven hours later, they had been identified according to a comment on the video by Mayor Luigi Brugnaro's account.
"We've spotted them," it said, adding that the surfboards had already been seized.
"Soon, without giving any further details, those responsible will be in our arms: they will be prosecuted as they deserve."
After being identified, the pair's surfboards were confiscated and they were fined 1,500 euros (NZ$2430) each, according to a statement from the mayor's office.
They will also face further action from Venice's attorney for damaging the city's reputation.
This is not the first time Venice has run into trouble with its tourists. After decades of over-tourism, the city has recently started introducing new rules and restrictions to try and manage the number and behaviour of tourists.
Swimming in the canals is banned as well as eating on the steps of certain monuments.
In 2019, two German tourists were fined $1600 for brewing coffee on the 430-year-old Rialto Bridge.
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.
