A US Embassy document, seen by Reuters on Tuesday, said Hernandez was wanted on charges that he participated in a drug-trafficking scheme between 2004 and 2022.
Hernandez, who was replaced as president last month by lefist Xiomara Castro, has pledged to cooperate with national police.
Among the charges, Hernandez, 53, is accused of participating in an operation to receive in Honduras tonnes of cocaine from Colombia and Venezuela, the document said. The cocaine was then to be shipped to the United States.
The embassy also said Hernandez - who was president from 2014 to 2022 - received millions of dollars in bribes in exchange for protecting traffickers from investigation and prosecution.Â
The firearms charges include carrying, using, or aiding and abetting the use of weapons, including machine guns.
The US State Department referred queries to the US Justice Department, which declined to comment. A spokesman for the US Attorney's Office in Manhattan declined to comment.
Honduras' Supreme Court - which will decide on the extradition request - met on Tuesday and appointed a justice to oversee the case. The process could last between two and three months, according to Hernandez's defence.
Hernandez had been holed up in his home, according to one of his lawyers, after about 100 police officers surrounded it late on Monday.
"The national police, through my proxies, have already received the message that I am ready to collaborate and voluntarily arrive with their accompaniment, at the moment the judge appointed by the honourable Supreme Court of Justice decides, in order to face this situation and defend myself," Hernandez said in a message on Twitter.
Just a few hours after leaving office, Hernandez joined the Central American Parliament (Parlacen), a six-country regional body that affords its members immunity from prosecution.
However, any immunity bestowed by Parlacen, which comprises elected officials as well as former presidents and vice presidents, can be removed or suspended at the request of a member's home country.
Security Minister Ramon Sabillon said on Tuesday that President Castro had ordered him to comply with the law and to keep her informed. A presidency source said Castro would not comment publicly until the Supreme Court had reached its decision.
Lawyers for Hernandez told a local TV channel that if a Supreme Court judge orders his client's arrest, he "is willing to surrender voluntarily".
Washington's request for extradition is in contrast to a period when the US government saw Hernandez as a vital ally in volatile Central America during his eight years in power.
However, expectations have grown in recent months that Hernandez would face an extradition request after leaving office.
Last year, a US judge sentenced Hernandez's brother to life in prison plus 30 years for drug trafficking and the former president was named as an unindicted co-conspirator in another drug trafficking case in New York.
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