The health region wouldn't give details, but CBC Newsworld is reporting that the woman gave birth to twins after fertility treatments in India.
The CBC says Ranjit Hayer's two boys were delivered seven weeks prematurely by caesarean section at Calgary's Foothills Hospital on Tuesday.
The mother is recovering in intensive care, while the twins are in neo-natal intensive care.
The CBC says one of the babies is breathing with the help of special equipment, but doctors say both boys are doing well.
The network quotes the woman's obstetrician, Colin Birch, as saying there are social and ethical considerations beyond the medical ones.
He says he can't imagine being 65 and having two five-year-olds running around.