Four militants carried out the attack, killing more than 10 people, the pro-Damascus TV channel al-Mayadeen said. Russia's RIA news agency reported that 15 people were killed.
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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.
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There was no immediate claim of responsibility for the attack. Footage broadcast by state TV showed bodies wrapped in shrouds at the scene and fire fighters putting out flames.
Previous suicide attacks in Damascus have been claimed by both Islamic State and the Tahrir al-Sham militant alliance, which is led by the group formerly known as the Nusra Front.
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