SANA news agency said the attack occurred near a vegetable market in Masaken Barzeh district on Tuesday.
The bomb attack is the latest in a series of bombings mostly claimed by the Islamic State (IS) terrorist group fighting to topple the Syrian government.
The death toll might rise because some of the injured were in a critical condition, The Syrian Observatory for Human Rights.
According to SANA, the club and the market are next to one another.
Syrian TV, quoting a source in the interior ministry reported that a car had tried to ram into the police officer’s club in the area, but was stopped by guards.
“A suicide bomber then detonated his explosives, causing deaths and injuries,” state television added, citing the source, without giving further details on the toll.
No group has so far claimed responsibility for the attack.