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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.

Belfast Magistrates' Court heard Catherine Strong subjected the elderly victim to a drunken attack as she lay in bed at their home in the city.
Strong, 49, of Argyle Street, Belfast, pleaded guilty to common assault on her mother.
She also admitted five assaults on police officers and police representatives.
When challenged by care workers who called at the house she was said to have become abusive and repeatedly shouted that her mother was dying.
Ordering full reports before she passes sentence, District Judge Fiona Bagnall said: "If those care workers had not come in goodness knows what might have happened."
A prosecution lawyer told how one of those who called at the home on 10 January had looked into the area where the victim's bed is located.
She saw the pensioner - believed to be in her late 70s - lying on her back with her feet hanging off the edge of the bed onto the floor.
"The defendant was standing over her mother holding a pillow in one hand," the prosecutor said.
"She was repeatedly striking her mother on the face and upper chest with the pillow."
The assault was said to involve pressing the pillow down on the victim's face for up to a second at a time, before lifting it up for the same period of time and then repeating the action.
In total the incident witnessed lasted for less than 30 seconds, the court heard.
It was stressed that the care worker believed Strong was beating her mother, but was not trying to suffocate her.
Strong, who was described as pleasant when sober but abusive when drunk, had been in an emotional state in the previous weeks.
She had repeatedly stated that her mother was dying, Judge Bagnall was told.
During the commotion at the house she also claimed she had been trying to put a pillow behind her mother's back.
She has cared for her mother since she had a stroke 12 years ago.
On the day of the incident Strong had drank a litre and a half of cider, but claimed to be more tired than drunk.
Strong also insisted she had a good relationship with her mother involving the pair joking and messing around, the court heard.
After hearing the details Judge Bagnall stressed the seriousness of the offence against a "vulnerable, elderly lady in care, a member of the family".
Pointing out that immediate custody could be imposed, she warned: "Be under no illusion, I'm taking this as having a fairly sinister set of facts."
A filly foal of racing legend Frankel has sold for an Irish record of 1.8 million euros (about £1.45m).
[NEXT_CONCEPT]
A woman who repeatedly pressed a pillow on her stroke-victim mother's face has been warned she could be jailed.