The kingdom, which has reported the highest number of coronavirus cases in the Gulf region, is scrambling to limit its spread.
With more than 50 confirmed infections in government-held areas, the Ministry of Human Rights has appealed for humanitarian assistance.
Under the terms of the agreement, MSF will assume the full management of the isolation centre for the duration of the current health crisis.
The Yemeni government has so far recorded 21 cases, with the Houthis reporting the first infection in Sanaa's administrative district.
The government has been working to establish quarantine centres as part of a plan to help up to 20,000 stranded Yemenis return home.
The UN agency has distributed ventilators and intensive care unit beds across Yemen to help the country battle the coronavirus pandemic.
A second spike in coronavirus cases is expected at the beginning of May after the government prematurely eased restrictions on movement, experts warn.
Years of conflict have destroyed healthcare infrastructure in embattled countries, leaving people vulnerable to infectious diseases.
Refugees are adhering to the government's quarantine and sanitary measures to prevent the spread of the COVID-19 disease.
A private Syrian airliner has been flying Russian-trained mercenaries to Benghazi, raising alarm that they may bring coronavirus into Libya.