According to gardaí, two men entered the pub on Faussagh Avenue in the Cabra area of the city's northside shortly after 7pm and opened fire.
A man in his 20s, reported to be convicted drug dealer Paul Cullen, was shot dead before the attackers fled the scene on a motorbike.
RTÉ also reports that the victim's family had thrown chairs at the gunmen during the attack.
As gardaí continue to probe the killing, local Fianna Fáil councillor Mary Fitzpatrick - who is also chair of the Dublin Central Joint Policing Committee - said the community was in shock.
"This is a truly awful event and the people of Cabra are horrified," she said.
"This cold blooded murder comes as a huge shock to the local community and undermines the good work being done, day in and day out, and sends the wrong message about Cabra."
Ms Fitzpatrick also demanded that Irish Justice Minister Alan Shatter give gardaí more resources to tackle serious crime.
"As chair of the Dublin Central Joint Policing Committee and founding member of the Cabra Community Policing Forum, I know the good work the local gardaí do with the local community to ensure a safe community for all," she said.
"The local gardai are on the case, but Minister Shatter needs to wake-up and realise that they are fighting serious crime and deserve to be provided with adequate resources to tackle serious crime."
Gardaí are specifically appealing to people who may have been in the Cabra House pub before or at the time of the shooting to come forward.
Officers would also like to speak to anyone who may have witnessed anything unusual or suspicious on Fassaugh Avenue around the time of the shooting.
A statement read: "Gardai are particularly keen to talk to anyone that may have seen a dark coloured medium sized motorcycle with a driver and a pillion passenger dressed in dark clothing, in and around Fassaugh Avenue at the time of the shooting or driving erratically near Fassaugh Avenue before or after the shooting.
"The driver of the motorcycle is believed to have waited outside the Cabra House while the gunman entered," the statement concluded.