A law enforcement official told CBS News that authorities in Washington State arrested the suspect, who will likely appear in court later on Tuesday.
At least four military bases, including the Naval Surface Warfare Center, received the suspicious packages, according to media reports.
The bases have not confirmed whether the packages were actually explosive, but media reports indicated they were all rendered "inert" by disposal teams at the bases.
Media reported one of the packages contained black powder attached to a fuse.
Earlier, officials announced that a series of suspicious packages were sent to several military bases within the Washington, DC. Packages were sent to the National Defense University at Ft. McNair; Ft. Belvoir; Joint Base Anacostia — Bolling; Naval Support Facility Dahlgren; the CIA and a Secret Service mail processing facility.