Jerry Corgnati said he is the temporary manager of Florida Swap Shop, the company that has run the drive-in and flea market.
Fun-Lan opened in January 1950 and could accommodate more than 650 cars, according to an ad printed in the Tampa Tribune.
There were more than 2,000 drive-ins across the country in 1987, according to data from the National Association of Theatre Owners.
At one point, the Tampa Tribune reported, Tampa had more than 25 drive-in theaters.
The company now belongs to his wife, Betty Henn, and has two locations in South Florida, in addition to the one in Tampa.
Daniel Angulo, a vendor at the flea market, said he was shocked when he heard he had to leave in a matter of days.