The discovery was made at Parson's Court in Newcastle at around 7.00pm on Friday.
The bodies of three children - two boys and a girl - were found in an upstairs bedroom.
The children are thought to be aged four, eight and 10-years-old.
Gardaí say they are investigating the circumstances of their "unexplained deaths."
The house has been sealed off for a forensic examination.
A woman aged in her 40s, understood to be the children's mother, has been taken to Tallaght Hospital.
Stephen Breen, crime editor with the Irish Sun, said it is understood a note was found at the house.
"There was a note recovered at the scene, it was on the window of the property.
"It's understood to have said 'Call 999 - don't go upstairs'.
"So it is quite concerning and will obviously form part of the Garda investigation".
"They also met with the children's families last night to inform them all of this devastating news.
"They will be continuing door to door inquiries today.
"[They] are also awaiting the results of a post mortem to establish how the children lost their lives.
"But they are of the belief that it wasn't through natural causes".
Anyone with any information in relation to this incident is asked to contact Clondalkin Garda station on 01-666-7600.
Gardaí say they are not looking for any other person in relation to this incident at this time.
