Nils Greskewitz, who police say is connected to militant environmentalist group Sea Shepherd, allegedly bent the harpoon part of the statue in Whale Beach Park on Monday, a force spokesman said.
Reports said he had been hanging off the harpoon part of the statue.
The German, who has been in Japan since Friday and had joined anti-whaling protests in the town, told police he had no intention of damaging the statue, Jiji Press said, quoting investigators.
The bronze statue, three metres (10 feet) high, was built in 1998 at the local park featuring a whaler throwing a harpoon from a boat, local media said.
The town drew worldwide attention after the Oscar-winning 2009 documentary "The Cove" showed how dolphins are corralled and slaughtered there. Activists continue to visit the town to protest.