Those freed include 42 survivors of an air strike on a prison in September that killed more than 100 people.
"The unilateral release of 290 detainees, including 42 survivors of an attack on a place of detention in Dhamar this month, took place today. The release was facilitated by the ICRC and the UN following a request from the National Committee for Prisoners Affairs," according to the statement.
"We are always ready to act as a neutral facilitator in the release of detainees when we receive a request from the parties to the conflict and hope that this operation opens the door to further releases to bring comfort to families awaiting reunification with their loved ones," said Franz Rauchenstein, the ICRC's head of delegation in Yemen, Xinhua news agency reported.
"The ICRC's role in this operation was, first, to confirm the identities of the detainees foreseen to be released and verify if they wished to travel straight from Sanaa to their homes or if they wished to be transferred to an area under the control of the other party," it added.
A prisoner swap was one of three elements of an agreement between the warring parties that was brokered by the UN in Sweden's capital, Stockholm, in December.
The head of the Houthi committee for prisoner-of-war affairs, Abdul Qader al-Murtada, had earlier said that the rebels would free 350 detainees, including three unidentified Saudi nationals. But later, the ICRC said it and the UN had facilitated the release of 290 detainees.
UN envoy for Yemen Martin Griffiths welcomed the move in a brief statement.
"I welcome the release of detainees by the Houthis and hope this will lead to initiatives to facilitate the detainees exchange as per the Stockholm Agreement. I welcome previous steps by the Yemeni government and Arab Coalition leading to release Yemeni minors," Griffiths said.
The Houthis urged the Yemeni government and the Saudi-led coalition to carry out the same step.
The Houthi militias and the Yemeni government agreed to exchange around 7,000 war prisoners in December 2018 as part of the Stockholm deal but they have since failed to implement it.
Saudi Arabia has been leading an Arab military coalition against Iran-allied Houthis in Yemen for over four years in support of the exiled internationally-recognized government of Yemeni President Abd-Rabbu Mansour Hadi.
( With inputs from IANS )