Seema Banu (37), her six-year-old son, Faizan Syed, and 11-year-old daughter, Asfira Riza, were found dead at their home in Llewellyn Court, Ballinteer, on October 28th.
The children were found to have been strangled, while Ms Banu died from a ligature around her neck, post-mortem examinations found.
On Saturday, gardaí investigating the murders confirmed they have arrested a man in his 30s.
He is currently being detained under the provisions of Section 4 of the Criminal Justice Act 1984 at Dundrum Garda Station. Investigations are continuing.
Earlier this month, a joint funeral was held for the mother and children at the Islamic Cultural Centre of Ireland in Clonskeagh.
The three coffins sat side by side as Imam Hussein Halawa said a number of prayers before they were taken to Newcastle Cemetery for burial.
Indian Ambassador to Ireland Sandeep Kumar posted on social media after their deaths: “The Embassy has offered full support to family and garda.
“It also expresses appreciation to the local community for rallying together and showing solidarity in a difficult situation.”
The bodies of Ms Banu and the children were discovered at the family home on October 28th after concerned neighbours raised the alarm.
It is believed they may have been dead for several days.
Gardaí made the grim discovery when they arrived on the scene.
They urged the public not to spread uninformed information via social media, saying it is unhelpful to the investigation.
Dozens of locals staged a candlelight vigil outside the family home hours after their bodies were found.
Investigators questioned a 36-year-old man who was known to the family in the days after their deaths, but he was not arrested.
Saturday’s arrest is the first to be made in connection with the killings.
