The bank, inaugurated in Rajasthan's Udaipur city, will provide "safe and pasteurised human milk" to children whose mothers are unable to feed them, the chief operations officer of the bank, R. K. Agarwal, told AFP.
It is believed to be the first such centre in north India, Agarwal said. Others operate in the south of the country.
"Foster mothers and wet nursing has been a tradition of India. It has been scientifically proved mother's milk is the ultimate and universal wonder drug for infants," said Agarwal, who is a paediatrician.
"The bank wants to make available this precious natural milk to as many infants as possible when their own mothers are not able to do so."
The Divya Mothers Milk Bank has been set up at a government hospital in Udaipur, 334 kilometres (208 miles) from state capital Jaipur with help from a non-profit organisation.
Breastfeeding is recommended for feeding babies, but mothers who give birth to preterm babies struggle to provide breast milk while others may be unable to produce it, Agarwal said.
Donor milk can also be a life-saving measure for babies, helping protect against infection and promoting growth, he said.
Agarwal said volunteers would ask lactating women in the area to donate their milk at the bank. The donor would be screened for various diseases and the milk would then be pooled and pasteurised before being refrigerated.
The World Health Organisation recommends exclusive breastfeeding for up to six months of age to help ensure good health and survival of babies.
One in three malnourished children worldwide is found in India, with 47 percent of under-threes underweight, according to UNICEF.