Pune's Guardian Minister Girish Bapat and the city civic body have ordered an inquiry into the incident.
The Sambhaji Brigade, which claimed responsibility for the alleged vandalism on social media, said that after removing the writer's bust from the garden maintained by Pune Municipal Corporation, its workers threw it in a river.
The outfit alleged that Gadkari, in his book and play 'Raj Sanyas', portrayed Chhatrapati Shivaji Maharaj's son Sambhaji Raje in poor light.
"We were seeking removal of the bust from the Sambhaji Garden and had done necessary correspondence with Pune Municipal Corporation. However, they paid no heed to the demand, prompting our workers to storm the garden and remove the bust," Sambhaji Brigade leader Santosh Shinde said.
"It is quite ironical the bust was installed in the garden, which was named after Sambhaji Raje. Such insult and defamation of Sambhaji Raje will not be tolerated," he said.
Shinde also said that those who vandalised the statue will surrender before police.
Meanwhile, the Deccan Gymkhana police registered a case against four persons in connection with the incident.
"We have registered a case against four members of Sambhaji Brigade for allegedly damaging public property and stealing the bust," Senior Police Inspector Ajay Kadam said.
He said they registered the case after the Sambhaji Brigade posted on social media about the vandalism, claimed responsibility for the incident and disclosed the names of its members, who allegedly executed the act.
"We have recovered a CCTV footage from near the garden and found that there were four persons who had removed the bust at around 2 AM," he said.
A team has been formed to nab the suspects, he said.