In a case that has increased tension between Washington and Moscow, Roman Seleznev was arrested in the Maldives last week and accused of stealing credit card data. Russia says he was, in effect, kidnapped.
Valery Seleznev, a member of Russia's lower house of parliament, denied the charges against his son and said he was being held in a jail on the Pacific island of Guam, where a Russian diplomat would visit him tomorrow.
He told a news conference his son needed medicine for a severe head injury suffered in 2011, adding: "He will die quickly if he doesn't take the pills for three or a maximum five days."
Anna Otisko, the detainee's girlfriend, said she had been on holiday with him in the Maldives but he was detained at the airport by people in shorts and check shirts and carrying backpacks. She said he had enough medicine for a week.
US State Department spokeswoman Jen Psaki has dismissed Moscow's accusations over the incident, saying: "Certainly, no kidnapping took place."
Mr Seleznev was indicted in Washington state in March 2011 on charges including bank fraud, causing damage to a protected computer, obtaining information from a protected computer and aggravated identity theft, the US agency said in a statement.
The indictment said Mr Seleznev hacked into websites run by Phoenix Zoo, a delicatessen and many other small restaurants and entertainment venues in the United States.