"People consider this audacious," he told Al Jazeera's Kristen Saloomey.
"They think 'What you come from Bangladesh to do banking in NYC? That sounds so ridiculous. This is [the] city where [the] whole world learnt banking from'."
But the Nobel laureate said New York also had its share of poor people just like any other city "so we are actually working in [a] third world" environment.
The bank and its founder earned the 2006 Nobel Peace Prize for helping thousands of poor Bangladeshis start their own businesses by offering them small loans.
"If this one works it will change the whole future of banking … in the whole world"
Muhammad Yunus, Grameen Bank founder
Grameen America is targeting millions without a bank account and those with limited access to financial institutions, particularly women, to put them on the road to self-sufficiency.
To qualify for a Grameen loan, borrowers must be part of a group that meets weekly on financial management, pay back a certain percentage plus interest and set aside some savings.
A default by one member will result in the whole group being cut off from future borrowings.
Wendy Brown, who started a cleaning business with her sister a year ago, stands to benefit from a small loan as she plans to expand her enterprise.
"It means a lot to me in terms of buying supplies and being able to operate my business. I bought a laptop," she told Al Jazeera.
"You get to network with a lot of women who aspire to do a lot of great things, a lot of ideas, you can feed from that as well."
Muhammad Yunus said every person possessed an enormous capacity and gifts "but they never have the opportunity to unpack that gift".
He added: "If this one works it will change the whole future of banking ... in the whole world."