In an opinion piece, Police Association Victoria Secretary Wayne Gatt expressed his concern about the lasting effect of enforcing "unpopular and deeply restrictive rules for a prolonged period" on the community's views of the force.
"Police are now tasked with enforcing a curfew that no one has welcomed, and to prevent families from going to playgrounds that bring them joy," he wrote in the Herald Sun on Wednesday.
"I hope that our members do not have to ever actively enforce this ban on playgrounds."
About 50 of the state's 227 active cases are aged 10 and under, including a child in intensive care, who is in a stable condition.
Chief Health Officer Brett Sutton said his team was probing a potential case of playground transmission, along with a "more definitive" link between students who walked home together.
"(The students) did not have any other face-to-face interaction other than sharing a walk home, didn't play together, don't live together, didn't have classes together," he told reporters on Tuesday.
Outdoor playgrounds, basketball hoops, skate parks and exercise equipment were closed and the city's 9pm to 5am curfew reimposed this week, in a bid to contain the state's worsening Delta variant outbreaks.
There are now more than 520 exposure sites in Victoria, including a Jacana skate park that was added as a tier two exposure site on Tuesday night
Health authorities are also pleading for residents of southeast Melbourne to get tested for COVID-19 as the city's mystery cases continue to grow.
The state recorded 24 new locally acquired coronavirus cases on Tuesday, with 10 potentially infectious while in the community.
The health department is asking anyone who lives or spends time in Glen Eira and Port Phillip local government areas to get tested if they have been to exposure sites, have any symptoms or "even if they are unsure".
Melbourne is 13 days into its sixth lockdown, which was extended on Monday until September 2.
