Ten people from two families, including a mother, father and a five-month-old baby, were killed in the blaze.
Five children under 10 are believed to be among the dead.
Archbishop Martin said the news was heart breaking for all in the Traveller and wider local community.
He has asked that all those who have died and those injured and their families be remembered in prayer at all Masses in the Archdiocese.
It is thought that the family was living at the encampment off the Glenamuck Road for around eight years.
The fire is being treated as a tragic accident.
A spokesperson from The Southside Traveller Action Group said their staff were in a state of shock at the devastating loss of lives: "Families gathered today at our centre in southside Dublin where we are doing everything we can to support them.
"We thank the gardai [the police] for their support at this time and appeal to the media to respect the privacy of the families of those who died."
Alex White, Minister for Communications, Energy and Natural Resources and TD for Dublin Rathdown added his comments, saying: "Our thoughts and prayers are with those who are currently battling with their injuries, and the families and friends of all those who died."
