He fled to a nearby trailer park, where he was arrested.
Forrest said a search of the Branchburg motel room where Woodson was staying turned up additional weapons, ammunition, a night vision scope, police scanner, and a map of a military installation.
FBI and the ATF agents from the Joint Terrorism Task Force are assisting in the investigation.
Investigators say they don't know Woodson's intentions, or if he was planning any kind of attack.
They believe he served in the navy, but has been out of service for several years. They are waiting to hear back from navy personnel about his history.
Somerset County Prosecutor Wayne Forrest said, "These are weapons that could penetrate cars, metal, bulletproof vests... these are weapons of mass destruction."
The prosecutor's office did not know if Woodson had retained a lawyer.