A Darwin business has been shut down after it allegedly breached health directions, including the Northern Territory's vaccine mandate, multiple times.

Police say they attended windscreen repair business Windscreens Territory after fielding several complaints from the public that staff were not wearing masks.

An indoor mask mandate has been in place across the NT for a week and a lockout enacted on Thursday means people who are not vaccinated can only leave their homes for essential goods, medical services or to provide care.

Police have alleged the owner of the Coconut Grove business and two staff who were working were not vaccinated, in breach of the lockout rules as well as a wide-ranging workforce vaccine mandate. 

Incident Controller Virginia Read said the business also failed to submit a COVID Safety Plan and was not keeping a vaccination register.

Fines of $5,024 were issued to each of the three people for the alleged breaches of Chief Health Officer directions.

The Chief Minister criticised the business in a short statement.

"I'm angry and every Territorian should be angry," he said.

"This is a gut punch."

Ms Read said police would continue to monitor compliance with health directions.

"The majority of Territorians are doing the right thing to help keep the community as safe as possible," she said in a statement.

"COVID-19 is now in our community but there are measures as outlined in CHO Directions that can limit the risk to public health.

"Police will continue to conduct compliance checks with a zero-tolerance approach."

Last July, a Darwin souvlaki shop was ordered to close for allegedly breaching health directions despite multiple warnings.

The Northern Territory joined several other jurisdictions in reintroducing restrictions this week as it worked to slow rapidly rising rates of community transmission.