The ICRC, whose representatives have visited Guantanamo detainees since January 2002, said that the video calls can last for up to an hour.
Families make the calls to their detained relatives at ICRC offices or national Red Cross/Red Crescent offices where they live.
A video link has been in place for US-held suspects at Bagram detention facility in Afghanistan since early 2008.
About 226 detainees from 28 different nations are being held at the prison camp at Guantanamo Bay, a US naval base.
The largest group of remaining detainees are Yemeni, followed by Afghans and Chinese Uighurs.
Barack Obama, the US president, said that he intends to close the prison camp by January 2010.
While some inmates will soon be released, others are expected to be tried in US federal courts or in US military commissions.