At a news conference Friday, the mayor said programs for children and the elderly will also take a hit, the Detroit Free Press reported.
The state had offered to take over management of Belle Isle, a 985-acre park in the Detroit River, assuming responsibility for $6 million in operating costs.
Because of other cutbacks, only 57 of the city's more than 300 parks will be open this summer. Officials said maintenance at the remaining open parks will be reduced.
The city is struggling with a $350 million budget deficit.
"We looked a gift horse in the mouth," Bing said. "We had a deal that was workable that would not have closed parks. ... When we thumb our nose at $6 million, I think it's nuts."
Brad Dick, the general services manager, said with no maintenance, the closed parks will look "pretty awful" once summer arrives.
"It's going to be tall weeds with trash in there," he said.