It comes after senior figures in NHS Grampian warned the region may not be allowed to move to level two with the rest of the country on May 17 if cases do not fall before then.
Moray currently has the highest rates of Covid in the country, with a seven-day positivity rate of 81.4 per 100,000.
East Dunbartonshire has the second highest with 41.4, while neighbouring Aberdeenshire and Highland are at 11 and Scotland as a whole sits at 21.4.
Scottish Government guidance indicates that an area must have fewer than 50 cases per 100,000 in order to be considered for level two restrictions.
Paul Southworth, consultant in public health at NHS Grampian, said: “The situation in Moray is continuing to worsen. Last week the rate was around 50 per 100,000 and that is rising rapidly. We have also seen an increase in covid hospital admissions from Moray this week.
“In the last seven days Moray has seen 55 per cent of Grampian’s cases – but has less than 17 per cent of the population.
“We’re continuing to see an upward trend and we are yet to see the impact of any mixing over the May Day weekend, so it is possible the situation could worsen in the coming days.”
Health bosses at Dr Gray’s Hospital, in Elgin, said local knowledge had indicated that some people were choosing to break the rules by entering other people’s houses and organising gatherings.
Jamie Hogg, divisional clinical director at Dr Gray’s Hospital, said: “The local population has done exceptionally well to this point and Moray has escaped the worst of the pandemic – it’s had lower numbers of cases, lower infection rates, it’s often been in lower levels – but that could be about to change.
“Anecdotally we’re being made of aware of people either with symptoms or who have been asked to self-isolate by contract tracers not doing so – our message today is simple, self-isolate or Moray will become isolated.
"The area will see further increases potentially leading to hospitalisations and possibly deaths. It is vital to protect each other, protect business and the wider region that people self-isolate and get a test when they have symptoms or when they are asked to do so by Test and Protect.”
Moray Council chief executive Roddy Burns said: “Ultimately if the situation continues to escalate we may find ourselves living with restrictions which could severely impact on our daily lives – affecting education, businesses being able to operate or using sporting facilities if rates continue to increase.
"We could either be left behind in terms of unlocking or even see other, stronger, restrictions imposed on the region.
“It’s vital that everyone continues to play their part in protecting each other, protecting businesses and ultimately protecting Moray.”
Tourism industry figures warned the rising levels of Covid-19 and fears the region could be subject to tougher restrictions than the rest of the country is already having an impact on local businesses, with holiday bookings being cancelled.