Concerned residents in the country and city are calling police to "dob in" people who flout anti-coronavirus restrictions.
Police are investigating a "high number" of suspected breaches by people and businesses.
A breakdown in the amount of reports against individuals, circumstances and regions was unavailable.
It was unclear whether fines had been issued in the state.
In response to growing concerns, police set up a plan with Health SA to prioritise calls to determine the most appropriate action which may include police attendance.
In the country, Barossa Local Service Area has dealt with a "small number" of reports and inquiries made by the public.
Officer-in-charge Chief Inspector Shane Addison said complaints related to business requirements and those failing to comply with the shutdown and social-distancing rules.
"We have had no reported non-compliance within Barossa LSA and no fines have been issued," he said.
Chief Inspector Addison said officers were being asked to conduct checks and were doing so as directed.
"In this task we are being supported by the group that the police have formed in the metropolitan area to conduct the majority of these checks," he said.
He explained how police seek compliance from people who have been required or directed to self-isolate.
Despite police concerns about the accelerated spread of the virus, overall Chief Inspector Addison said he had been "very pleased" with cooperation by residents regarding quarantine.
"I ask that everyone keep themselves informed of the latest developments and follow the hygiene, health and self-isolation advice provided by the state and federal government health services," he said.