According to intitial reports, three shots were heard in the basement of the building, which is a combination of a gym and barrack. There are no reports of injuries.
Fox 5 San Diego reports that three nearby schools are on lockdown.
The U.S. Navy could not immediately confirm the report.
The facility has a staff of more than 6,500 military and civilian personnel, and aims to provide medical care to military service members, their families, and those who served in the past, according to its website.
"We're not taking any chances and are executing procedures we've been trained for in this kind of situation," Naval Medical Center spokesman Mike Alvarez said.