By Michelle Roberts
BBC News, Health reporter in Lyon
Should the girl opt to use the eggs and gain regulatory approval, she would effectively have a baby that was her half-brother or sister.
Critics said the work, presented at a fertility conference in Lyon, was deeply concerning.
But the doctors from the McGill Reproductive Center, Montreal, called the donation an act of motherly love.
Also, the girl and any future partner would have a choice as to whether to use the eggs or not, they said.
The girl, Flavie Boivin, cannot have children naturally because of a chromosomal condition called Turner's syndrome.
Desperate to help, mum Melanie, who is 35 and a lawyer, investigated whether she could donate her own eggs.
After much research, she came across Professor Seang Lin Tan's team at McGill who run an egg freezing programme for cancer patients and those who want to delay childbearing.
Melanie said she discussed the decision with her partner and Flavie's father, Martin Cote, also 35 and a financial analyst.
"We were concerned about the ethical questions - would I look at the child as my grandchild or as my own? We were also concerned about the financial impact, the physical impact on me and the emotional impact on the family."
After a year they decided to go ahead.
Comment on Reproductive Ethics
"What made us sure was the fact that I was there to help my daughter. If I could do anything in my power to help her I had to do it and because of my age I had to do it now.
"I told myself if she had needed another organ like a kidney I would volunteer without any hesitation and it is the same kind of thought process for this."
Melanie said her daughter would be the real mother as she would be caring for the child.
"I do not want to oblige her to use the eggs; I want to give her the option."
Professor Tan said they had asked for the advice of an independent ethics committee.
"The ethic committee agreed to it because the mother giving to a daughter is out of love and it is up to the daughter and partner in future years to decide whether to use the eggs or not.
"And ethical considerations change with time. Who knows what the ethics will be in 20 years from now."
Professor Tan said this was the first case of mother-to-daughter egg donation. There have been cases of donation from sister to sister.
Dr Richard Kennedy, of the British Fertility Society, said: "This altruistic behaviour is not dissimilar to the scenario where a parent donates a kidney to a child.
"In this case, instead of using eggs from an unknown donor, she will get the opportunity to know the source.
"Although this means the resulting offspring will be similar in genetics, an unrelated sperm will be used - and this means that the offspring will not be a true sister."
Josephine Quintavalle, of Comment on Reproductive Ethics, expressed sympathy with the family, but could not support storing the mother's eggs.
She said: "The psychological welfare of the baby itself has to be the principal concern.
"Such a baby would be a sibling of the birth mother at the same time as the direct genetic offspring of the grandmother donor.
"In psychiatry we are hearing more and more of children suffering from identity problems, and specifically a condition called 'genealogical bewilderment'. Could it possibly get more bewildering than this?
"We have to stop thinking of women only in terms of their reproductive potential."The daughter could live a full and happy life without having children of her own."