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The horse, a daughter of Finsceal Beo, was bought at Goffs sales by Dermot Farrington for an unnamed Irish client.
It is the highest amount paid for a foal at public auction in Ireland.
Frankel was retired in 2012 after winning all 14 of his races, while Finsceal Beo (which means 'Living Legend' in Gaelic) won the 1,000 Guineas in England and Ireland in 2007.
The first foal of Frankel to be sold at auction went for £1.15m in London in June. The European record for a foal belongs to My Typhoon, a half-sister to Galileo and Sea The Stars, who sold for 1.8m guineas (£1.89m) at Tattersalls in 2002.
Six foals were initially due to go through the sales ring on Thursday, but there were two late withdrawals.
Two of the remaining foals went unsold with bidding at 350,000 and 650,000 euros respectively, while another fetched 550,000 euros.
Another four Frankel foals will go on sale next week at Tattersalls in Newmarket, just a few miles from where the stallion was born and now stands at stud for a breeding fee of £125,000 a time.
A filly foal of racing legend Frankel has sold for an Irish record of 1.8 million euros (about £1.45m).