The blasts killed two people and injured six others, it said, citing the Interior Ministry.
ISIS later claimed responsibility for the attack.
Two suicide bombers tried to storm the police command centre and clashed with guards before detonating explosive devices outside on Khalid bin al-Walid street, the Damascus police chief said on state TV.
Police forces then chased down the third attacker, who blew himself up nearby at the entrance of a clothes market.
“Our investigations are ongoing to find out where they came from and how,” Mohammad Kheir Ismail said from outside the headquarters. “The issue has been controlled.”
ISIS' media unit Amaq earlier reported the attack without outright claiming responsibility for it.
Earlier this month, militants struck a police station in another part of Damascus, with 17 reported dead in that suicide bombing which ISIS claimed.
The capital has enjoyed relative security as Syria’s six-year war has raged on nearby and across the country. But several such attacks have hit Damascus in recent years, including a car bomb that killed 20 people in July.
ISIS and Tahrir al-Sham – led by militants formerly linked to Al-Qaeda – have each claimed separate suicide blasts that killed scores of people in Damascus before.
“The desperate suicide attempts come as a response to the victories of the Syrian Arab Army and the Interior Ministry is fully ready to thwart any terrorist act,” state television quoted the minister as saying.
Syrian troops and allied forces have captured several suburbs of Damascus from rebel factions over the past year. The army and its allies have been fighting insurgents in the Jobar and Ain Tarma districts on the capital’s eastern outskirts.
