Santaniello said, however, that those account holders won't be left in the lurch.
"People won't be left without a means of receiving their federal benefits," Santaniello said. "The feedback we're getting from banks is that transitioning customers to other accounts is working well."
About 100,000 people will likely be affected by the program's closure.
When Treasury launched the program in the late 1990s, it was a way for consumers without a bank account to have their checks reach them electronically instead of in paper form. And since 2013, Social Security benefits must be received electronically.
More from Investor Toolkit:
Scammers create a new form of theft: 'Synthetic-identity fraud'
How well do you know your Social Security retirement benefits?
Volatility is here — but it's not the main risk for investors
While not all banks have offered the accounts, those that did were given a government subsidy. The accounts were required to meet a variety of federal guidelines, including a maximum monthly fee of $3 and at least four free cash withdrawals each month. However, check-writing and recurring automatic bill payments were not allowed.
Although this program is disappearing, another federally sponsored option remains available: the DirectExpress debit card.
With this, your Social Security payment (or other federal benefit) is put on your card, which comes with no monthly fee and can be used to make purchases, pay bills or withdraw cash.