Yankel Rosenthal, a former minister of investment, was arrested on Tuesday after landing at Miami airport.
His cousin Yani and uncle Jaime Rolando, a four-time presidential candidate and newspaper owner, were also charged.
They come from one of the wealthiest families in Honduras.
The three men were detained by customs officials when they landed at Miami airport on Tuesday morning.
They appeared before a federal judge in Miami on Wednesday.
The three men provided "money laundering and other services that support the international narcotics trafficking activities of multiple Central American drug traffickers and their criminal organisations," said the US Treasury Department in a statement.
Seven of their businesses were labelled under the US Kingpin Act as "specially designated narcotics traffickers".
They have been accused of transferring drugs money between accounts in New York and Honduras between 2004 and 2015, according to the Efe news agency.
Their lawyer, Andres Acosta Garcia, was also arrested at Miami airport on Tuesday and charged.
Yankel Rosenthal served as minister in President Juan Orlando Hernandez's administration but left the post unexpectedly in June.
During his term, he led Club Deportivo Marathon to several league titles.
He also built a brand-new stadium in the north-western city of San Pedro Sula which was named after him.
The president of one of Honduras's most famous football clubs has been charged in the United States with drug trafficking and money laundering.