The winning numbers were 07-21-22-25-28.
As it is a EuroMillions prize it will take a number of days to collect the prize money from affiliates.
The victor, who is remaining anonymous for now, can expect to pick up their cheque within the next fortnight.
National Lottery spokeswoman Miriam Donohoe said: "We would love to hear from them". We are making arrangements for them to come in and pick up the winning prize. It'll be within the next two weeks.
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Dolores McNamara, from Limerick, was Ireland's first and biggest EuroMillions victor scooping over £102 million in 2005.
This EuroMillions jackpot was the third win in Ireland in 2017. What a great way for a player to start the New Year.
The jackpot is being collated in the nine European countries that play the EuroMillions and the lottery expects the funds to be ready by Thursday or Friday.
"Nobody has come forward yet and we are now appealing to players in the Dublin region who bought a EuroMillions ticket last week to check their numbers to see if they are eligible to claim a cool €38,906,715", said the spokesperson. "We don't know if it's a single victor or a syndicate".
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"We are urging all our players to check their tickets to see if they are the lucky victor or winners", the spokeswoman said. The lucky star numbers were 1 and 12. EuroMillions players in Ireland won more than €170 million in prize money a year ago, including last Friday's €38.9 million jackpot.
It was the third Irish EuroMillions jackpot win during 2017 and the 12th overall.
The winning Quick Pick ticket was sold on Friday, December 29.
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