The fire started about 1:20 p.m. inside a shaft at 26-19 Jackson Ave., according to a Fire Department spokesperson.
One person was hurt, but the victim's injures aren't life-threatening, the agency said in a tweet.
Firefighters closed the avenue to traffic between 44th Drive and 43rd Avenue while they battled the blaze, which took over three hours.
The fire was under control by 4:20 p.m., according to the FDNY.
Fire marshals are investigating how the fire started.