Environment Minister Sussan Ley pulled out of a speech on Sunday after contracting cold symptoms.
The move by the Environment Minister followed her being at a Cabinet meeting last week with Home Affairs Minister Peter Dutton who later tested positive to coronavirus.
However, Ms Ley said she had been told it was not necessary for her to be screened for COVID-19.
"I've had a bit of travelling over the past week and I developed some mild cold symptoms on Friday evening," Ms Ley said.
"Following both the health department advice, and personal advice I sought from a doctor over the weekend, it was indicated that I don't fit the criteria for testing.
"I am however being particularly cautious in this environment, as I think people should be, and I don't want to risk passing cold-like symptoms on to anyone, particularly in situations where there are elderly people.
"I am certainly well enough to keep working but will continue to monitor symptoms and follow all guidelines, as I hope everyone does."
Ms Ley was due to speak at St Matthew's Church in Albury on Sunday.
Meanwhile, the Independent member for Shepparton Suzanna Sheed suggested her parliament, which reconvenes on Tuesday, sit remotely due to the virus.
"Hope the Victorian government are doing everything necessary to enable the parliament sitting week to be done via technology," Ms Sheed tweeted on Saturday.
"I'm in the risk group and want to stay with my community."
Member for Benambra Bill Tilley said the parliament did not have the ability for such a move and called for the houses to sit from Tuesday to Thursday as scheduled.
"We've had a Spanish flu and two World Wars and the parliament was never closed down," Mr Tilley said.
"What the parliament can do is minimise its exposure to coronavirus but...democracy has to continue to work, I'm very firm the parliament should not go into closure."
However, Mr Tilley will not be in parliament this week due to bushfire recovery work at Corryong.
Member for Ovens Valley Tim McCurdy said there had been speculation parliament could be cancelled beyond Tuesday and he would be disappointed if that occurred.
This is the last sitting week before May when parliament is due to resume with the delivery of the state budget.