The ferry was bought for $500,000 in 2007 as a backup to the main ferry that shuttles thousands of tourists to the former military base off lower Manhattan. But it would cost at least $6 million to replace steel and make other repairs.
It also costs about $20,000 a month to maintain the ferry.
Governors Island placed ads to sell the ferry in November but received no offers. New York state's Office of General Services plans to auction it off on eBay.
The island a half-mile from Manhattan is evolving into a public playground, attracting bicyclists and occasional concertgoers.
The state and city commissioned more elaborate development plans a year ago, but financing is uncertain.