It was the first time a woman has acted as a surrogate mother for her daughter in Japan, local media reported.
The case is set to stir debate in Japan where surrogate births are opposed by the government and a key medical group.
Japan's justice ministry also views the woman who gives birth as a child's mother - not the biological mother.
This legal position has led a Japanese celebrity couple to go to the courts to try to win the right to register twins born to a surrogate mother as their own children. Their case is continuing.
Adopted
Yahiro Netsu, the head of the Suwa maternity clinic in Nagano, told a news conference that the woman gave birth last year, Reuters reported.
She had agreed to in vitro fertilisation and to act as a surrogate mother because her daughter had had her uterus removed due to cancer and was therefore unable to bear children.
Both the mother and child were reported to be in good health.
Dr Netsu said the woman had first registered the baby as her own and then the child was adopted by her daughter and son-in-law.
The doctor, who has helped other couples to have children through surrogate mothers, called on the government and the medical authorities to review their stance against surrogacy.
Surrogate births involve removing an egg to be fertilised and then implanting it in another woman who carries the baby to birth.
