The robbery attempt was reported at 12:47 p.m. at the Bank of America at 200 East Franklin St., city spokeswoman Kim Bui-Burton said.
Police responded and took a suspect into custody near the intersection of Munras Avenue and Webster Street, Bui-Burton said. Officers found a suspicious package there and the suspect told officers about another package left at Washington and Pearl streets.
Streets around downtown Monterey were closed and businesses evacuated as the Monterey County bomb squad responded to inspect the packages.
Later in the afternoon, the packages at Washington and Pearl streets and at Munras Avenue and Webster Street were "detonated" and investigators checked their contents, Bui-Barton said.
The bomb squad also checked the suspect's vehicle, found at the Calle Principal Garage at 468 Calle Principal near West Franklin Street, Bui-Barton said.
No suspicious items were found in the vehicle, Monterey police said.
Officials have not elaborated on what the suspicious packages contained or why they were considered dangerous.