WTA chief Steve Simon was unwilling to speculate about future tournaments after it was announced the Indian Wells Open would not go ahead as scheduled.
Organisers announced on Sunday that the ATP and WTA Tour events at Indian Wells would not go ahead, just days out from when they were due to start, over fears about the coronavirus.
The coronavirus, which has killed more than 3,600 people worldwide, has impacted numerous sporting events.
Simon, the WTA chief executive and chairman, said it remained to be seen what would happen to future tournaments.
"First and foremost, there isn't anything more important than protecting the health of our players, staff, volunteers and fans who attend our events," he said in a statement.
"Based on the medical advice received on March 8, it is with regret that the 2020 BNP Paribas Open will not be held as scheduled this March. The WTA empathises with those affected by the coronavirus in this region and around the world.
"We are disappointed our fans will not be able to come out and watch the event, and our players are also disappointed to not compete over the next two weeks, along with the sponsors who support the event.
"However, we understand the decision which has been made in the interest of public health and safety, which is the top priority at this time.
"It is too soon to speculate about what will happen to other tournaments that follow. We will continue to closely monitor the situation. Health and safety will always come first."
Tournament director Tommy Haas said he was open to holding the event at a different time in 2020.
The Abierto Zapopan is scheduled to start in Mexico on March 16, eight days before the Miami Open is due to begin in Florida.