The worker, whose identity wasn't immediately released, was injured at 63 Flushing Ave. about 10:30 a.m., the spokeswoman said.
The person was treated at Methodist Hospital and listed in stable condition, officials said.
It wasn't immediately clear how the worker was hurt or if the person worked in construction or was just a staff member at the facility.
Officials with the Brooklyn Navy Yard didn't immediately respond to a request for comment.
The Department of Buildings received a complaint on July 7 that a worker had been injured there previously, but when an inspector showed up, staff there said no one had been injured there in the past two weeks, records show.