The Bharatiya Mahila Bank, which begins with seven branches, will employ women, accept deposits from and lend mostly to women.
The bank plans to open 500 branches all over India by 2017.
Just 26% of women in India have an account with a formal financial institution, compared with 46% of men.
That means an account in either a bank, a credit union, a co-operative, post office or a microfinance institution, according to a study by the World Bank.
Mr Singh opened the first branch in Mumbai’s Air India building on Tuesday.
“Both men and women can open accounts. But the bank will be predominantly for women in accepting deposits and giving loans. Our main objective will be to empower and educate women financially,” Usha Ananthasubramanian, chairperson of the bank, told BBC Hindi’s Rupa Jha.
The bank will also open branches in villages, where women face more problems opening an account.
In February, the federal government announced the launching of the bank with initial capital of $184m (£116m).
Finance Minister P Chidambaram had said the bank would employ women, lend mostly to women and “address gender-related issues, empowerment and financial inclusion”.
Correspondents say many Indian women typically give their earnings to their husbands – when in fact women are seen as more astute savers than men and it would make sense for them to have a bank account of their own.
Only 35% of Indians have access to banking services against a global average of 50%.
There are only around 100,000 bank branches in India and a large number of the country’s more than 650,000 villages do not have a single bank.
Photo and Article from BBC Business.