Chief Magistrate Maxwell Gicheru granted the four bail to enable them seek medical attention.
Baktash Akasha, Ibrahim Akasha, Vijay Goswami and Hussein Shabakash told the court they were suffering from life threatening medical conditions in making their application to be freed on bail.
The formal extradition process has already commenced for the four who are wanted in the United States over an international drug cartel.
A warrant of arrest was issued against the four by a US court over narcotics importation conspiracy charges.