Police used sniffer dogs to carry out searches at The Arches, where Regane MacColl, 17, had collapsed last month.
The men, who were aged between 21 and 26, were escorted from the nightclub in the early hours of Saturday morning.
Last month, Ms MacColl, of Clydebank, near Glasgow, fell ill after she was thought to have taken an ecstasy-style pill known as 'mortal kombat.'
A Police Scotland spokesman said: "Fourteen men, aged between 21 and 26, are the subject of a report to the Procurator Fiscal for alleged drugs offences following a search of patrons at a city centre night club on Saturday 1 March."
Following Ms MacColl's death, the venue's management introduced an over-21s policy for club events to 'ensure a safer clubbing environment' for its customers.
As a result, more than 1500 people signed an online petition in protest to the move by the management.
Meanwhile, staff have reiterated their commitment to detering drug use at the club.
A spokesman said: "The Arches fully co-operated with this police operation and the arrests further emphasise our zero tolerance approach to drugs within the venue."
More than 500 mourners attended Ms MacColl's funeral service at St Mary's Church in Clydebank.
She had been a sixth year pupil at St Peter The Apostle High, Clydebank.