In a message to Trump, Xi, 67, said that after learning US President Trump and Melania have tested positive for COVID-19, he and his wife Peng Liyuan extend sympathy to them and wish them a speedy recovery, state-run Xinhua news agency reported.
The US and China have sparred over the origin of the virus for days, with a Chinese official promoting conspiracy theories.
Under the policy, the US recognises and has formal ties with China rather than the island of Taiwan, which China sees as a breakaway province to be reunified with the mainland one day.
Donald Trump on Wednesday started his maiden visit to Beijing with both sides inking deals worth $9 billion.