The arrest was made last night.
24-year-old Andy Cash has been charged with the murder of Lisa Cash (18), and twins Christy and Chelsea Cawley (8), who were killed this weekend.
Andy Cash is the brother of the three siblings.
The three siblings were found dead at their home in Rossfield Avenue in Tallaght on Sunday morning. Another brother, who is aged 14, raised the alarm of the incident and escaped out the window. He is being treated for his injuries at Tallaght Hospital.
As RTÉ reports, Andy Cash appeared before a special sitting of the Dublin District Court at the Criminal Courts of Justice last night. He had been arrested earlier in the evening.
He was charged with all three murders and replied no comment to each one as they were said aloud.
His defence solicitor has requested a psychological assessment and solitary confinement in custody, but Judge McNamara said that that would be a matter for the prison governor.
No bail has been granted, and he will remain in custody. On 9 September, he will appear via video link at the Cloverhill District Court.