Mr Ban’s younger brother and his nephew stand accused of offering money to a Middle Eastern official, through an American middleman.
They allege the two men bribed the official to use state funds to buy their building project.
Mr Ban served as UN secretary general from 2007 until 2016.
He was succeeded by former Portuguese Prime Minister Antonio Guterres on 1 January 2017. Mr Ban is now being seen as a possible future president in his home country of South Korea.
Prosecutors say that in early 2013 the South Korean construction firm Keangnam, of which Mr Ban’s brother Ban Ki-sang was an executive, was faced with growing debt and sought to sell a building complex in Vietnam known as Landmark 72.
In a 39-page indictment unsealed on Tuesday at a Manhattan courthouse, prosecutors alleged that he and his son Joo Hyan "Dennis" Bahn, a Manhattan estate agent, stood to make millions of dollars in commission on the sale, valued at up to $800m (657m pounds).
周二，曼哈顿法院开庭时呈上的39页起诉书中，检察官指控潘基文弟弟Ban Ki-sang和他的儿子Joo Hyan Bahn（一名曼哈顿房地产经纪人）设定百万美金佣金出售该建筑，佣金价值高达800万美金。
US officials say that the two men paid millions of dollars in bribes and tried to trade on the prominence of their South Korean family name in order to persuade a Middle Eastern official from an unnamed country to arrange a purchase of the complex by that country’s sovereign wealth fund.
Federal papers say the two even tried to secure a meeting to discuss the deal with that country’s head of state during his visit to New York during an annual UN general assembly meeting.
Mr Bahn, who has pleaded not guilty, was released on bail.
According to the indictment, a $500,000 initial bribe was paid to US businessman Malcolm Harris who presented himself as an agent of the official, with another $2m promised upon the closing of the sale.
But Mr Harris allegedly double-crossed Mr Bahn and his father and made off with the money. Neither Mr Harris nor Mr Ban Ki-sang have been detained.