She needed chemotherapy, which damages the ovaries, before receiving a bone marrow transplant from her brother at Great Ormond Street Hospital in London.
So, before treatment, when she was 9, she had her right ovary removed in an operation in Leeds, where the tissue was frozen.
Specialists were able to preserve the organ, in the hope it would allow her to one day have a family.
This story originally appeared on the Daily Telegraph.
The ovary remained frozen until last year when specialists arranged for it to be sent to Denmark, where the transplant took place.
The patient and her husband, Ahmed, then underwent IVF to increase their chances of pregnancy.
Al Matrooshi, whose son was delivered at the privately-run Portland Hospital today, said: "It's like a miracle. We've been waiting so long for this result - a healthy baby.
"I always believed that I would be a mum and that I would have a baby," the new mother said. "I didn't stop hoping and now I have this baby - it is a perfect feeling."
Her doctor, Sara Matthews, a consultant in gynaecology and fertility, said: "This is a huge step forward. We know that ovarian tissue transplantation works for older women, but we've never known if we could take tissue from a child, freeze it and make it work again," she told the BBC.
After the ovarian tissue was first removed, it was mixed with cryo-protective agents and stored under liquid nitrogen.
Last year, surgeons in Denmark transplanted five slivers of the ovarian tissue back into her body - four were stitched on to her failed left ovary and one on to the side of her uterus.
At 23, the young woman had been going through the menopause. But after the transplant, her hormone levels began returning to normal, she began ovulating and fertility was restored.
The couple then underwent IVF treatment to maximise the chance of pregnancy, resulting in the production of three embryos, two of which were implanted earlier this year.
Dr Matthews said: "Within three months of re-implanting her ovarian tissue, Moaza went from being menopausal to having regular periods again.
"She basically became a normal woman in her 20s with normal ovary function."
Professor Helen Picton, who leads the division of reproduction and early development at the University of Leeds, carried out the ovary freezing.
She described the breakthrough as "incredibly encouraging".
She said the procedure to take the tissue back in 2001 happened long before any baby had been born from ovary tissue preservation.
"Worldwide more than 60 babies have been born from women who had their fertility restored, but Moaza is the first case from pre-pubertal freezing and the first from a patient who had treatment for beta thalassaemia," she said.
