Patrick Nulty has confirmed he is resigning as a TD with immediate effect.
Mr Nulty issued a statement saying he had sent "inappropriate messages via Facebook", including "inadvertently sending one to a 17-year-old woman" whom he said he has never met.
The 31-year-old said he sent the message "under the influence of alcohol".
Mr Nulty apologised "wholeheartedly to the woman involved and to her family".
He said it was never his intention to upset anyone in this way but "it was totally wrong".
He added that he takes "full responsibility" for his actions and for this reason he has decided to resign his seat in the Dáil.
Mr Nulty said while he set himself the highest standards personally and politically, he has not met those standards in this matter.
He said he believes resigning is the "correct and right course of action".
In the statement, Mr Nulty thanked his supporters, friends and family and also apologised to his constituents in Dublin West for his "mistake".
He has said he will not be making any additional comment on the issue.
He made the decision to resign after the Sunday World newspaper put questions to him about the matter.
Mr Nulty was elected to the Dáil in 2011 in the Dublin West constituency for the Labour Party.
He resigned from Labour in June 2013 when he accused the party's leadership of bringing the political system into disrepute by sacrificing core democratic social demands for personal political ambitions.
He lost the party whip in December 2011 when he voted against the Budget.