All the windows of the centre were blown out and technicians were on site to investigate the cause of the blast.
The centre was located in the basement of a building in Fittja, in southwest Stockholm.
"No one was inside. No one was injured. It had been locked since earlier in the evening," a police spokesman said.
No one has been arrested and there are currently no suspects, he added.
Earlier on Wednesday, 28 people were killed and dozens wounded in Turkey's capital Ankara when a car laden with explosives detonated next to military buses near the armed forces' headquarters, parliament and other government buildings.
