Thanh Cong Phan, who lives near the northwestern city of Seattle, was taken into custody after the FBI "determined that the packages contained potential destructive devices and appeared to be sent by the same individual," an FBI statement said.
The agency said that multiple packages had been received at facilities on Monday in and around Washington, including the Central Intelligence Agency's headquarters at Langley and the Fort Belvoir and Fort McNair military bases.
The suspect was due to appear in federal court in Washington state later Tuesday.
Speaking to reporters at the Pentagon, US Defense Secretary Jim Mattis confirmed that no one had been injured by any of the material in the packages, which were intercepted by the FBI.
However, the FBI warned that more packages could have been sent and were still awaiting processing, urging caution.