Halima Cisse gave birth to the nonuplets in Morocco. Mali’s government flew her there for specialist care.
“I’m very happy,” her husband told the BBC. “My wife and the babies [five girls and four boys] are doing well.”
A woman who had eight babies in the US in 2009 holds the Guinness World Record for the most children delivered at a single birth to survive.
Two sets of nonuplets have previously been recorded – one born to a woman in Australia in 1971 and another to a woman in Malaysia in 1999 – but none of the babies survived more than a few days.
World record holder Nadya Suleman’s octuplets have grown up and are now 12 years old. She conceived them through in vitro fertilisation.
Fanta Siby, Mali’s health minister, congratulated the medical teams in both countries for the “happy outcome”.
Ms Cisse’s pregnancy became a subject of fascination in Mali – even when it was thought she was only carrying septuplets, the Reuters news agency reports.
Doctors in the West African nation had been concerned for her welfare and the chances of the babies’ survival – so the government intervened.
After a two-week stay in a hospital in Mali’s capital, Bamako, the decision had been made to move Ms Cisse to Morocco on 30 March, Dr Siby said.
After five weeks at the Moroccan clinic, she had given birth by Caesarean section on Tuesday, the minister said.
Her husband Adjudant Kader Arby is still in Mali with the couple’s older daughter, but he says he has been in constant touch with his wife in Morocco and says he is not worried about the family’s future.
“God gave us these children. He is the one to decide what will happen to them. I’m not worried about that. When the almighty does something, he knows why,” he told BBC Afrique.
He says the family has been overwhelmed by the support they have received.
“Everybody called me! Everybody called! The Malian authorities called expressing their joy. I thank them… Even the president called me.”
The mother and her new nine babies are expected to return home in several weeks.