BEIJING—A leading Chinese health official said that a newly identified virus originating in central China has spread between humans, heightening health officials’ concerns that it could be transmitted even more quickly as the number of confirmed cases tripled on Monday.

The prospect of human-to-human transmission of the coronavirus, which causes a potentially deadly pneumonia that already has claimed four lives, comes as tens of millions of Chinese citizens crisscross the country this week for the annual Lunar New Year holiday....