"Since he is still without symptoms the authorities advise that he has not knowingly put others at risk, although anyone he has been in contact with prior to Thursday afternoon has been notified and will be tested if they show any symptoms of the virus.
"We want to assure everyone that Richard is feeling well and still without symptoms."
The confirmation comes after Wilkins came in close contact with Rita Wilson, who has tested positive for coronavirus, in Sydney last week when she appeared on Today Extra.
Wilkins also met with Wilson, who is currently in isolation at Gold Coast University Hospital with husband Tom Hanks, during her show at the Sydney Opera House last weekend.
Today Extra hosts David Campbell and Belinda Russell are both currently in self-isolation because they came in contact with Wilson on Monday at Channel 9.
Both hosts have tested negative for the coronavirus, a Channel 9 spokesman said.
Earlier on Sunday, Today show weatherman Tim Davies announced he will be missing from the Channel 9 breakfast show for the next two weeks due to self-isolation.
Davies was on his way home to Australia after a holiday in Austria when Prime Minister Scott Morrison announced on Sunday afternoon that all passengers arriving in Australia have to self-isolate for 14 days in a bid to stop the spread of coronavirus.
The Channel 9 presenter posted a photo of himself on Instagram from a plane at Dubai International Airport with the caption: "So, I'm on one of the first international flights to land in Australia tomorrow where everyone on board will be required to self-isolate for 14 days.
"This is the right move by our government. Passengers don't seem angry, panicked or confused by this move.
"My @thetodayshow family has been fantastic & I'll be back on air after a bit of a 'longer than expected' break."
