Militants targeted the station in the al-Midan neighbourhood and clashed with police officers there, Interior Minister Mohammad al-Shaar said in comments broadcast by state television from the police station.
One attacker blew himself up at the main entrance and another detonated his explosive device on the first floor, he said.
The blasts damaged the lower floors of the building and shattered the windows on one side.
Footage broadcast by state TV showed bodies wrapped in shrouds at the scene and fire fighters putting out flames.
Ambulances had previously rushed to the blast site while security agents cordoned off the area.
There was no immediate claim of responsibility for the attack.
Previous suicide attacks in Damascus have been claimed by both Isis and the Tahrir al-Sham jihadist alliance, which is led by the group formerly known as the Nusra Front.
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