The alert comes as former US Vice President Al Gore is expected in Gothenburg to receive a prize for his environmental work. Crown Princess Victoria is also due to visit the city.
The post terminal, on Kruthusgatan in the city, was raided just after 1am by men armed with rifles. Several suspected bombs were found after the robbers left the scene. Police sealed off a large area following the discovery.
Police say the post office staff on duty were forced to the ground by the robbers, who then disappeared with their loot.
Around ten people were working at the facility at the time. Nobody was injured and it is unclear whether anything of value was taken.
Five minutes before the police were alerted to the robbery a car was parked outside Gothenburg's main police station. Guards at the entrance saw two men running from the car and disappear in another vehicle. Just after 3am an object was seen in the car that looked like it could be a bomb.
Another suspected bomb was found in a car outside the City Police Station's vehicle entrance on Färgaregatan. Another suspect device had been chained to a gate at the police station.
The robbers set light to four cars and spread caltrops - metal 'crows feet' designed to puncture car tyres - across Kruthusgatan as they made their escape. Police found another suspect device near one of the burning cars.
Witnesses reported seeing the robbers' getaway car. The vehicle was found burnt out shortly after the raid, and the robbers are believed to have continued their escape in another, as yet unidentified, car.
At 4:30am police started to evacuate Färgaregatan. Shortly after 6am bomb disposal experts had still not arrived at the scene. At 7am police cordoned off a larger area outside the police station. Skånegatan, one of the most important routes in and out of the city, was closed in both directions.
Local residents were faced with long delays as they made their way to work. One resident, Jessica Edin, left her apartment on Folkungagatan at 6:30am to be greeted by police cars with flashing lights. Police were standing all around, stopping people on their way to work or to local bus and tram stops.
"This really feels a bit weird," was Edin's reaction.
Police officers and civilian police employees were gathering at the Ullevi conference centre during the morning while they waited for the suspect devices to be defused.