Luas operators Transdev are urging passengers to contact them when seeing evidence of drug-taking on the tram.
Their advice comes after a woman told listeners on Joe Duffy's Liveline programme that she saw a drug addict inject himself in the groin after dropping his trousers. while travelling on the Luas.
The incident was not reported to the Luas operators - but they stressed that swift action would be taken if they were informed.
The incident, which is alleged to have occurred last Thursday at 3pm, left two young women who were sitting beside him in "shock".
Speaking on RTE's Liveline programme, Cliona Coughlan told host Joe Duffy that she "felt a bit sick" when the man injected himself in the groin after pulling down his trousers.
"Last Thursday me and my friend were going shopping and we were sitting on the Luas and this guy came along and we knew from the start he was kind of a drug addict," she said.
"He was walking up and down and breathing really heavily.
"He sat down beside this young guy and I couldn’t really see what he was doing.
"He then got up and sat beside my friend – she had her back to him – so she couldn’t really see what happened and he just started injecting himself with heroin," she added.
She said around 30 people were in the Luas carriage.
"We kind of got a bit of a shock because they were so close and then we didn’t want to draw attention because obviously we don’t know what could happened," Cliona said.
"He sat down and started preparing more of it and put it into tin foil and it was kind of a bit of a shock to see something like that happening on the Luas."
The incident occurred on the red Luas line.
The women did not report the incident to Gardai or the driver.
Communications manager of Transdev Ireland Dervla Brophy confirmed they had not received a report about the incident, and said swift action would have been taken if they had been made aware.
"When something like this happens it is imperative that people report this type of incident to the driver or one of the ticket inspectors," Dervla told independent.ie.
"In this situation we would ask the person to leave the train, look at the CCTV and call the gardai to come and take them," she added.
She insisted this would be an incident that would merit their collaboration with Gardai to examine CCTV footage and could possibly take the Luas involved out of service.