The man who died reportedly lived in a unit on the first floor of the building, where the fire is suspected to have started, said Deputy Fire Chief Geoff LaTendresse.
The man's identity has not been released. As of about 8 a.m., the Alameda County coroner's bureau had not been contacted.
Of the 16 units at Pennsylvania Apartments, four had significant smoke damage. The rest of the units suffered heavy smoke damage.
Several pets were missing from the complex, located at 3600 Pennsylvania Ave., LaTendresse said.
Firefighters from Union City, Newark and Hayward were called to assist with the blaze that was first reported at about 7 a.m., said Fremont Fire Department Battalion Chief Mark Neveau.
The fire was controlled at about 7:25 a.m. and some of the firefighters were being released at about 8:15 a.m., LaTendresse said.
Investigators are trying to determine the cause of the blaze, LaTendresse said.
