Callejas, who was president of Honduras from 1990 to 1994 and head of the country's football federation until August this year, faces eight charges of racketeering, fraud and money laundering.
The 72-year-old Callejas, a current member of FIFA's Television and Marketing Committee, was remanded into custody.
He is accused of receiving $1.6 million in bribes between March 2011 and January 2013 for broadcast rights of games played by the Honduran national team.
US authorities early this month accused him and 15 other current or former soccer officials from Latin America of wide-ranging graft, much of it related to alleged bribery in attributing TV and marketing rights to FIFA games, especially in Latin America.
The US allegations against Callejas and the other defendants were made public on December 3, the same day Swiss police in Zurich arrested two FIFA vice presidents in Zurich.
The arrests were carried out at the five-star Baur au Lac hotel, a favorite of FIFA's officials and the same spot where seven football executives were arrested in May on charges of corruption at FIFA dating back decades.
A total of 39 people and two companies have been charged by US authorities in connection with the scandal. About a dozen have pleaded guilty.
Callejas, who appeared in court in Brooklyn wearing a checkered shirt and jeans, left Honduras on Monday on a private jet to face justice in the United States.