The WTA and ATP Tour events were due to start on Wednesday and Thursday respectively, but organizers announced they would not go ahead amid concerns for the safety of players and fans.
The Riverside County Public Health Department declared a public health emergency on Sunday after a confirmed case of coronavirus.
Tournament director Tommy Haas said he was open to holding the event at a different time in 2020.
"We are very disappointed that the tournament will not take place, but the health and safety of the local community, fans, players, volunteers, sponsors, employees, vendors, and everyone involved with the event is of paramount importance," he said in a statement.
"We are prepared to hold the tournament on another date and will explore options."
Professor of medicine and biomedical engineering at the University of Southern California, Dr David Agus said: "There is too great a risk, at this time, to the public health of the Riverside County area in holding a large gathering of this size.
"It is not in the public interest of fans, players and neighboring areas for this tournament to proceed. We all have to join together to protect the community from the coronavirus outbreak."
The coronavirus has killed more than 3,800 people worldwide, with more than 110,000 confirmed cases.
There have been more than 500 confirmed cases in the United States, with 21 deaths.