Daljinder Kaur gave birth to a baby boy, whom she named Armaan, on April 19.
"God heard our prayers. My life feels complete now," Kaur told AFP. "I am looking after the baby all by myself. I feel so full of energy. My husband is also very caring and helps me as much as he can."
Kaur had been regularly visiting a fertility clinic with her husband of 46 years, Mohinder Singh Gill, 79, for two years.
During that time, Kaur attempted to conceive using in vitro fertilization.
"When we saw the (IVF) advert, we thought we should also give it a try, as I badly wanted to have a baby of my own," she said.
Doctors were unsure whether Kaur was a good candidate for childbearing, considering her age, but tests said otherwise.
"I first tried to avoid the case because she looked very frail. Then we made her undergo all the tests and once all the results were OK we went ahead," Anurag Bishnoi, who runs the fertility clinic, told AFP.
Kaur's exact age was also unknown. In a country where birth certificates are uncommon, she guessed that her age was 70, but the clinic said in a statement that she was 72.
"People (ask) what will happen to the child once we die, but I have full faith in God," Gill said. "God is omnipotent and omnipresent. He will take care of everything."
Armaan weighed about 4.4 pounds at birth and is said to be "healthy and hearty," AFP reported.