The announcement comes on the second day of a unilateral two-week ceasefire announced by the Saudi-led coalition supporting the government in what it said was a move to help fight the pandemic.
"The first confirmed case of coronavirus has been reported in Hadramawt province," Yemen's supreme national emergency committee for Covid-19 said on Twitter.
The committee, run by the internationally recognised government of President Abedrabbo Mansour Hadi, said the infected patient was in stable condition and receiving care.
It said medical teams and concerned authorities had taken all necessary precautions and promised to release further details later on Friday.
Following years of war and Saudi-led military intervention, Yemen already faces what the United Nations describes as the world's worst humanitarian disaster.
Aid groups have warned that when the coronavirus does hit the country's broken healthcare system, the impact is likely to be catastrophic.
Tens of thousands of civilians have been killed over the past five years in the war between the coalition and the Iran-backed Huthi rebels, who control large parts of Yemen including the capital Sanaa.
Cholera widespread
Millions have been displaced and diseases including cholera are widespread due to the scarcity of clean water.
Despite two decades of air and drone strikes by the United States, Yemen also still hosts a significant jihadist presence, with a longstanding Al-Qaeda network challenged in recent years by militants loyal to the Islamic State group.
Control of Hadramawt province, where the first coronavirus case was reported, has long been divided. Coalition-backed government forces control the coastal towns but parts of the interior remain in the hands of Al-Qaeda.
The coalition said it was observing a unilateral ceasefire to help efforts to prevent a Covid-19 outbreak in Yemen.
"The coalition is determined... to support efforts towards combatting the spread of (the) COVID-19 pandemic," coalition spokesman Turki al-Maliki said on Wednesday.
The move was welcomed by the United States but dismissed by the Huthi rebels who charged that continued air strikes by the coalition showed its announcement was a coronavirus public relations stunt.
"We consider the ceasefire a political and media manoeuvre," Huthi spokesman Mohamed Abdelsalam told Al Jazeera news network.
The United Arab Emirates, a key Saudi ally, said that the battle against the coronavirus trumped all other concerns.
"The COVID-19 crisis eclipses everything -- the international community must step up efforts & work together to protect the Yemeni people," UAE Minister of State for Foreign Affairs Anwar Gargash tweeted.
UN Secretary General Antonio Guterres has repeatedly appealed for ceasefires in conflicts around the world to facilitate the battle against the coronavirus.
The UN envoy to Yemen Martin Griffiths said last week he was engaged in talks to secure a nationwide ceasefire.
Griffiths said he was in regular contact with both sides "on reaching agreements on a nationwide ceasefire, humanitarian and economic measures to alleviate the suffering of the Yemeni people".
"This process further aims to foster joint efforts to counter the threat of COVID-19," he said.
Saudi Arabia is also scrambling to limit the spread of the disease at home. Its health ministry has reported more than 3,200 coronavirus infections and 44 deaths from the illness.
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