Dr Chant has come under fire over her handling of the state's latest outbreak, with cruel trolls attacking her appearance and demeanor at press conferences.
Anthony called on his 125,000 Instagram followers to exercise compassion and calm during the lockdown.
"This is not a political post but one of compassion. There’s a lot of talk about Dr Kerry Chant wiping her eye with her mask in the daily NSW press conference," he captioned a photo of the health expert.
"I don’t know about you but whether you agree with the NSW government stance, their approach and their reaction to the current outbreak, I just think we need to remember this person is a human being. A human being with feelings.
"I honestly don’t envy her job and her responsibilities and don’t want to even imagine the red tape, political agendas and questioning she would have to endure and deal with.
"I honestly look at this pic and want to ask her “are you ok?” Not laugh and want to rip her to shreds."
The 38-year-old singer, who recently appeared on Celebrity Apprentice Australia, said the situation in Sydney is "truly heartbreaking".
"To all my friends and family in Sydney and anyone reading this who is in Sydney, please stay safe and REALLY do the right thing!
"This doesn’t only affect Sydney/NSW but the entire country and so many industries….and with the numbers where they are, this isn’t going away anytime soon!"
The ARIA award-winning performer said he hopes Australia can catch up to other countries' vaccination rates "sooner rather than later".
Anthony knows all too well the struggles of lockdown after suffering through 112 days of at-home isolation last year with his husband-of-seven years Tim Campbell.
"With my husband and I being Victorians, the lockdown was definitely not fun or easy," he said at the time.
"New music helped get me through 2020, with releasing songs ‘Lonely’ and ‘Shadows’."