The experimental technique has been tested on a group of infertile women who reached the menopause at around the age of 30.
Of the 13 treated women, one has given birth to a healthy boy and another is said to be pregnant.
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Until now the only option available to women with this form of infertility has been to accept IVF treatment using donor eggs, which means raising a child with another biological mother.
The researchers plan to see if the technique can help other categories of women, including those affected by cancer treatment, and who become infertile between the ages of 40 to 45.
About 1% of women have a condition called primary ovarian insufficiency which brings on the menopause at a very young age.
On average the women taking part in the study were 37 years old and had stopped menstruating 6.8 years earlier.
The "In-Vitro Activation" (IVA) technique involves removing the ovaries, cutting them into small one to two millimetre square cubes, and treating the fragments with special stimulating drugs for two days.
The fragments are then implanted within the Fallopian tubes and hormones administered to trigger egg development.
Lead scientist Dr Kazuhiro Kawamura, from St Marianna University School of Medicine in Kawasaki, Japan, said: "For patients with primary ovarian insufficiency, egg donation is the only option for bearing a baby.
"These patients are eager to find a way to become pregnant with their own eggs. I hope that IVA will be able to help patients with primary ovarian insufficiency throughout the world."