At least one pharmacy, which reportedly stocked the medicine, has been shut down and its owners detained.
The deaths occurred between Friday and Sunday. Officials say they were mostly drug addicts in Shahdra town area.
Cough syrup, which is sold as an over-the-counter medicine, is sometimes used by addicts to get high, police say.
“Some of the victims were found dead in a graveyard where addicts used to take different kind of drugs,” says local Police Chief Atif Zulfiqar.