The Arab Coalition said on Wednesday that it will release seven Houthi prisoners to reciprocate the release of a Saudi soldier, amid an international push to revive Yemen's political process.
Houthi officials on Tuesday approved the release of prisoner Mousa Awji, whose health condition is deteriorating.
Mr Awji was returned on a plane facilitated by the International Committee of the Red Cross (ICRC) from Sanaa to Riyadh, Houthi officials reported.
"We are pleased that this person has now returned home and we continue to offer our services so that thousands more people can return to their families," said Fabrizio Carboni, ICRC Regional Director for the Near and Middle East.
It is unclear if Mr Awaji is the first prisoner to be released under a deal agreed between the Saudi-backed government and rebels at United Nations-brokered peace talks in Sweden last month.
The Yemeni government and Houthi rebels agreed to exchange 15,000 detainees during peace talks in Sweden last month.
“This is an important step to continue building confidence among warring parties in Yemen”, Mr Carboni said.
The two sides submitted lists of prisoners to the UN mediators after meeting with the ICRC in Amman this month to finalise the agreement, but they are yet to agree on the full terms of the swap.
The operation is regarded as one of the least contentious confidence-building measures agreed during talks last in December as pressure mounts to end the conflict.
The development comes as UN chief Antonio Guterres held a phone call with the Saudi Crown Prince Mohammed bin Salman on Tuesday night.
The two discussed progress on resolving the war in Yemen and other regional issues, according to the Saudi Press Agency, SPA.
“The Secretary-General of the United Nations expressed his gratitude for the Kingdom’s support in pushing for positive results in the dialogue between the Yemeni parties,” SPA reported.
The international body is aiming to salvage a peace deal struck to implement a troop withdrawal from the port city of Hodeidah.
It is the main entry point for Yemen’s commercial and aid imports.
Meanwhile, UN special envoy to Yemen Martin Griffiths said the truce in Hodeidah "is holding", adding that the Arab Coalition remains committed to reaching a political deal to end the war.
The official has visited Yemen several times this month to discuss ways to overcome the obstacles facing the agreements made in Sweden.
Speaking on BBC Radio 4, Mr Griffiths stressed that gaining access to Hodeidah, the withdrawal of forces and the resumption of UN-sponsored meetings between the two sides would be vital to ensuring the implementation of any political process.
A UN-led redeployment co-ordination committee (RCC), aimed to bring together the rival military leaderships, will restart its meetings within the next few days, he said.
The international body is pushing to pave the way for a second round of discussions to end a nearly four-year-old war that has killed tens of thousands of people.
Houthi rebels still maintain control of Hodeidah and troops that are part of the Arab coalition are massed on the city's outskirts.
Mr Griffiths urged the warring parties to withdraw from the province, while acknowledging that the proposed timeline of January 7 for a pullout from the port was not a realistic demand.
The development comes as Houthi rebels shelled a public school in Taez, killing a student and injuring another on Wednesday afternoon.
The conflict in Yemen has triggered what the UN calls the world's worst humanitarian crisis, with millions of people at risk of mass starvation.
The war has killed some 10,000 people since the Saudi-led coalition intervened in support of the beleaguered government in March 2015, according to the World Health Organization.