Nuala Conway gave birth to four girls and two boys on 22 May. One of the girls passed away at a local hospital, publicist Max Clifford confirmed.
"Our hearts go out to the mum and dad and we hope that the others are going to be fine," he said.
Mrs Conway, from County Tyrone, gave birth to Ursula, Austin, Shannon, Karla, Eoghan and Kerrie in Belfast. It was Kerrie who died.
Speaking on BBC Radio Ulster Mr Clifford said: "Ironically Kerrie, and one of the other sextuplets, were moved from the Royal Victoria in Belfast because they were considered to be the strongest and doing best of all."
"They were moved from there to a local hospital, and tragically Kerry died last night.
FROM BBC RADIO ULSTER
"Two months on, the others are all gaining weight and seem to be fine as was Kerrie until sadly this happened."
Mr Clifford said he had spoken briefly to the family and they were "distraught."
Mrs Conway and her husband, Austin, live at Dunamore near Cookstown.
Speaking in June, she said that they had been told risks of proceeding with the birth and given the option of aborting some of the foetuses.
"But we knew without discussion what we both wanted. These babies are a wonderful gift from God," she said.
"Whatever God laid out for our lives, we were taking it," she told the Sunday Express newspaper.
The chairman of Cookstown District Council, SDLP councillor Tony Quinn, said the community would be devastated at the news of the death.
"The whole community was so happy and thrilled, first when the babies were born and then as their health began to improve," he said.
"Now sadly one has lost its fight for life and my heart goes out to the family. They have the thoughts and prayers of everyone in the community."
Mr Quinn said the community would offer whatever support it could to the family.
The babies were delivered by Caesarean section and were 14 weeks premature. They weighed between 1lb 7oz and 2lb 2oz.
It was the first recorded birth of sextuplets on the island of Ireland, and the first in the UK since 2001.
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