She gave birth to the twin boys by Caesarian some two weeks ago at the hospital in canton Graubünden's chief town of Chur, where all three are still under observation.
While Switzerland only permits IVF treatment if parents are young enough to be able to accompany their child through to maturity, Ukraine provides IVF treatment regardless of age.
The unnamed sexagenarian mother plans to raise the children in her four-room apartment in the village of Grüsch in Graubünden. The former Protestant cleric is the oldest woman known to have given birth in Switzerland and will be 84 by the time her children come of age.
"It's incredible what medicine can do nowadays. I want to enjoy this event now in peace," newspaper SonntagsBlick quoted her as saying.
But the births have outraged many, with one commentator in the Swiss newspaper Le Matin attacking the woman for her "selfishness" and "irresponsibility", saying that her twins, named Joshua and Michael, would be spending their teenage years ensuring their mother has a place in an old people's home.
A neighbour in Grüsch echoed the sentiments, telling SonntagsBlick, "It's pure selfishness, and not good for the children."
Indignation was also the main reaction on internet chat forums on Monday.
“We must accept certain limits of nature and keep common sense in mind,” Dr. Olivier Irion, chief medical officer of the department of obstetrics and gynaecology at the University Hospital of Geneva told Le Matin.
In vitro fertilisation should be reserved for younger women with problems conceiving, he added.
But Lorenz Casutt-Peng, the deputy mayor of Grüsch welcomed the birth, saying, "Children are our future and it's a good thing that both the children and their mother are doing well."
Online news website Blick has queried whether Swiss nationals should be able to get around the law on IVF by travelling to another country for fertilisation. The Protestant Church also believes the Swiss law should be respected.
“Whoever decides after due consideration to make use of this technique should be free to do so. But only if it complies with statutory limits,” Philippe Woodtli, director of the Federation of Swiss Protestant Churches told Blick.
Pregnancy among women in their sixties is increasing, news website Le Matin reported. In the past five years, four mothers over the age of 60 have given birth in Switzerland alone.
"In general, the desire for pregnancy is occurring later than in the past," said Dr. Irion.
The previous record in Switzerland was held by a woman who was 64 when she had a baby girl, while reports suggest that the world's oldest new mother is an Indian woman who gave birth to twins at the age of 70.