Navy officials on Monday identified the sailor as 25-year-old Juan Gerardo Medina-Reynaga. Stars and Stripes reported that he was a petty officer third class.
Medina-Reynaga was a native of Kansas assigned to USS George H.W. Bush.
Investigators say security personnel stopped a 2016 Dodge Charger that was being driven erratically on the Virginia Beach military base Friday night.
Officials say Medina-Reynaga sped away from the traffic stop, hitting a gas pump while trying to avoid an automatic barrier.
Medina-Reynaga then led security officers on a foot chase that ended in a struggle. Officials say he was shot after assaulting security personnel and trying to take a weapon from a security officer.