Uniform patrols in the Dublin Region, with support from armed patrols including the Garda Armed Support Unit, have been increased in response to the incident.
Gardai have also appealed to the public not to share videos from the scene in the aftermath of the violent incident, and to be aware of “a significant level of speculation, misinformation and disinformation”.
The scene remains preserved as a technical examination is carried out by the Garda Technical Bureau.
Gardai said that no arrests have been made.
Irish Taoiseach (Prime Minister) Leo Varadkar said he was “shocked” to hear about the shooting at “a well known family restaurant I’ve visited many times”.
“Full Garda investigation under way. My thanks to them and solidarity to staff and customers,” he said on Twitter.
Justice Minister Helen McEntee said that the attack taking place where families had gathered was “disgusting.
“I deplore the violence in Blanchardstown tonight.
“This viciousness has resulted in unimaginable human suffering this Christmas,” she said on Instagram.
“That anyone could perpetrate such violence as families gathered together is especially disgusting.
“I’m thinking of the bereaved, those who were at the scene and indeed all the emergency service personnel working tonight and over Christmas who have to deal with this senseless violence.
“I call on anyone with information of any kind to contact An Garda Siochana.”
An incident room has been established at Blanchardstown Garda Station and the investigation is being led by a Senior Investigating Officer (SIO).
The Garda National Bureau of Criminal Investigation is also providing assistance and a Garda Family Liaison Officer has been appointed to both families.
“An Garda Siochana is aware of videos of the incident and immediate aftermath which are in circulation on social media and messaging apps,” Gardai said in a statement.
“We are appealing to the public for these videos not to be further distributed.
“We are also appealing to the public to be aware of a significant level of speculation, misinformation and disinformation which is in circulation.”