People told by NHS Test and Trace to self-isolate could give their contact details to police.
The Department of Health and Welfare (DHCS) said that police forces will have access to information "on a case-by-case basis" so they can know if a person has been asked to self-isolate.
The DHSC updated its online guide on how to handle coronavirus test data on Friday.
Those who fail to do so will face fines from £ 1,000 and up to £ 10,000 for repeat offenders or serious violations, the DHSC said.
Individuals who test positive must isolate for 10 days after showing symptoms or their test date if they have no symptoms, while members of their household must isolate for 14 days.
A DHSC spokesman said: "It is a legal requirement that people who test positive for Covid-19 and their close contacts, self-isolate when officially asked to do so.
“The Department of Health and Welfare has agreed a memorandum of understanding with the National Police Chiefs Council so that police forces can access information on a case-by-case basis to determine if a particular person has been notified.
“The Memorandum of Understanding ensures that information is exchanged with appropriate safeguards and in accordance with the law. No test or health data is shared in this process. "