"These are practices worthy of the Soviet era, when people were treated as mentally ill when all they did was voice their disagreement with the official line," the RSF statement said.
Karimov, who is the nephew of the Uzbek president, disappeared on September 12 after visiting his mother at Jizzakh hospital.
Khaidarov was arrested two days later and charged with extortion. Investigators say he faces up to 10 years in prison.
Both men have been working for foreign-based media critical of the Uzbek government.