Another first in transplants may happen soon if the embryo implanted into her body successfully embeds in her uterine wall, and the unnamed woman could be the first in the world to give birth from a transplanted womb.
The doctors successfully introduced an embryo into the woman that they grew from her own egg. Though the woman's ovaries are intact and can produce eggs, she was born without a womb as she suffers from congenital disorder MRKH syndrome.
Another important aspect of the transplant is that the woman has received her mother's womb. And if all goes well, it could mean that the child would be the first one to be born from the womb from which her mother emerged.
The unidentified woman is one of the nine women to receive womb transplants in Sweden between September 2012 and April last year.
"The best scenario is a baby in nine months," said Dr Mats Brannstrom, professor of obstetrics and gynaecology at the Sahlgrenska Academy, Gothenburg, Sweden, who led the transplant team.
He also said that if the procedure turns out be successful then it could be a breakthrough in curing uterine infertility.
Thousands of women with the same problem in Europe have pinned their hopes on the new development. But the method has generated some controversy as it involves taking wombs from living donors.
Dr Mats Brannstrom said it is not possible to establish the chances of success as the procedure is new and if they do not get lucky this time, they may plan some more trials. But fertility experts are of the view that risks involved in the entire procedure are too great.
In a similar case, a woman in Turkey conceived after a womb transplant in 2011, but the trial failed as she suffered a miscarriage.
MRKH syndrome affects one in 5,000 women which prevents the womb from developing.