People in England who have been told to self-isolate through NHS Test and Trace could have their details shared with the police on a "case-by-case basis".
Forces will have access to information telling them if an individual has been told to self-isolate, the Department of Health and Social Care (DHSC) said.
But the British Medical Association said it was worried police involvement might put people off being tested.
In England there is a legal requirement to isolate after a positive test.
Police will not have access to data from the NHS Covid-19 app. The app is anonymous so the government does not know who has been sent instructions to self-isolate.
Just under 11% of people traced as a close contact of someone with coronavirus said they self-isolated for 14 days, according to a government-commissioned study.
Reasons given for breaking self-isolation included believing there was no point isolating from strangers if you cannot properly distance from those in your household; not developing symptoms; or visiting shops or a pharmacy.