The opposition members have been in custody for three weeks since a violent clash erupted between the National League for Democracy and government supporters.
Voice of America reported the ICRC team will leave Sunday from Yangon, formerly Rangoon, to meet the organization's members, held in an undisclosed location.
Despite international pressure to free Suu Kyi, the NLD leader, Myanmar has refused to allow the ICRC to see her.
Among those supporting her release are foreign ministers of the Association of Southeast Asian Nations, U.S. Secretary of State Colin Powell, Philippine President Gloria Arroyo and Amnesty International.
NLD won the 1990 elections, but the military would not recognize the vote. Since then, Suu Kyi has been in and out of detention.