On the ATP Tour, the Shanghai Masters is the most high profile event to have been called off.
WTA chairman Steve Simon said the WTA was "extremely disappointed".
"We do however respect the decision that has been made and are eager to return to China as soon as possible next season," he said.
ATP chairman Andrea Gaudenzi said: "We respect the Chinese government's decision to do what's best for the country in response to the unprecedented global situation.
"These important events have been a cornerstone of the Tour's presence in Asia and I want to thank the organizers for their commitment and cooperation. Chinese fans are some of the most passionate in the world and I know players will be looking forward to the next opportunity to play in front of them."
The ATP Tour is currently set to resume from 20 August with the Cincinnati Open and the US Open scheduled to take place back-to-back in New York.
The WTA Tour is set to resume with the Palermo Open on 3 August, marking the return of top-level tennis after the professional tours were suspended because of the pandemic.