Wilkins also took the opportunity to criticise the Government's "irresponsible" stance on asymptomatic coronavirus patients.
"The suggestion is that days after the last symptom, people should 'assume' that they're over this thing and proceed with caution.
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"I find this totally unacceptable and irresponsible! I completely understand the fact that the last thing the Health Department wants to do is spend days retesting people like me and God knows that I don't want to soak up resources.
"But I don't see how I can walk out my front door until I have a clean bill of health! I know the health system is fighting a huge battle and resources are stretched.
"But in clear conscience … I can't put others at risk … until I'm assured that I'm not positive anymore."
Wilkins revealed he had tested positive when he got checked after coming in close contact with Rita Wilson before she was confirmed to have coronavirus in Sydney earlier this month.
The Nine presenter also met with Wilson during her show at the Sydney Opera House. She was later put in isolation at Gold Coast University Hospital with husband Tom Hanks.
Speaking on the Today show from quarantine shortly after news of his result broke, a shocked Wilkins explained he had no symptoms.
"You could have knocked me over with a feather last night when I got the call. I feel fine. I feel 100 per cent. I don't have a sore throat, runny nose, headache. I feel terrific. Yet I contracted the thing and tested positive for it," he told hosts Karl Stefanovic and Ally Langdon.
"We're assuming this is from Rita. It may not be. They said it could be anyone, anywhere, any time, such is the prevalence of this thing," he said.
Describing the diagnosis as "terrifying", Wilkins appeared emotional as he described telling his children the news. "Having to call my kids and tell them this stuff wasn't much fun. The weird thing is the only thing you want to do more than anything in the world is hug your kids at a time like this."
