A fire damaged the storage shed at the on Stow Street recently.
Director John Idone said the suspected arson caused an esimated $4,000 in damage to the building.
"We've been having some vandalism problems down at Kramer Fields here in the last month," Idone said. "We had removed all the equipment from that building."
In the past month, vandals threw a bicycle rack onto the storage shed's roof, flipped over a set of bleachers, broke into the concessions building and set some leaves on fire.
Idone said they suspect the fire that damaged the shed is arson because the building caught fire in the middle of the night with no accelerants or flammables inside.
The building is a wooden structure 10 feet by 30 feet in size.
The Kramer Ball Fields have been closed since city engineers determined the bridge across the Cuyahoga River to the fields — the park's only access point — was not safe for use.
Idone said the plans for the bridge's replacement should be done by the end of the year with construction to start as early as March 2013 with the ball fields to reopen in 2014.
"So next season will be the last season it's closed," he said.
The damaged storage shed will most likely be rebuilt but not until the ball fields are ready to reopen.
As for the vandalism, Idone is hopeful this latest incident will be the last.
"The police have stepped up their enforcement in that area, so hopefully it's the last of it," he said.