SHANGHAI—The U.S. State Department said Sunday that it is organizing a single flight out of the central Chinese city of Wuhan, confirming efforts to extricate diplomats and a limited number of private U.S. citizens from the virus-hit city.

In an email to U.S. citizens in China also posted to its website, the State Department said a flight would leave Wuhan on Tuesday and fly to San Francisco. It invited U.S. citizens with a valid passport to contact the U.S. Embassy in Beijing. Private citizens are expected to later repay...