Franco Rocchetta, a former junior foreign minister, has filed a formal police complaint over the exhibition which included the Musee d'Orsay's Olympia on its first trip away from Paris since 1890.
But the superintendent for Venice's cultural heritage, Renata Codello, said the organisation of the show had been monitored and no "irregularities" were found.
Rocchetta claimed builders made "30-35 holes" of up to seven centimetres in diameter in the walls of the historic palazzo, Italian news agency ANSA reported.
He also said a dent had been made in the floor of a formal reception room once used by the "doges" - the city leaders who governed Venice for centuries.
"The damage to the flooring has been hidden by a table from the bookshop," he said in the complaint.
Two members of the city council said they were filing a formal request for more information from the mayor.
If the allegations are confirmed "this would be very serious," said one of the two, Simone Venturini.
"It doesn't matter how important the exhibition, the Doge's Palace is a treasure that we have to preserve and pass on to future generations," he said.
The Edouard Manet exhibition is the first time Olympia was exhibited next to Titian's Venus of Urbino, which inspired the French painter.