In a briefing note to staff, NHS Grampian said it had been recording an “exponential” growth in cases of the virus in the past fortnight which was expected to continue.
Modelling by the health board, which serves around 500,000 people in the north east, showed that “even more significant pressure” on hospitals and care homes was likely to follow.
“Our planned response will include a declaration of a major incident when a number of key trigger points are reached,” the briefing note read.
It said this would be determined by factors such as the number of Covid patients in hospitals across the region and the levels of staff sickness related to the virus.
The note warned that the major incident could be declared “as early as the end of next week” and was expected to last for around 30 days, with delays to non-urgent procedures likely.
The warning was issued as the latest group of UK military personnel began arriving in Scotland to support the NHS, which is facing unprecedented pressure.
A total of 38 servicemen and women have been deployed in NHS Grampian, with 32 others in NHS Lanarkshire and 20 in NHS Ayrshire & Arran.
The NHS Grampian group are expected to be deployed as healthcare support workers and nurses in the emergency and intensive care departments.
The Military Assistance for Civilian Authorities (Maca) support was approved by the Scottish Government in December.
Hundreds of members of the Armed Forces have already been supporting the vaccine programme across Scotland, as well as driving ambulances.
Scotland’s Health Secretary Humza Yousaf thanked the military for its support, adding: “The next few weeks are going to be extremely challenging for the NHS on a number of fronts.
“We have the pandemic backlog that has built up, together with high levels of staff absences, again much of that because of Omicron and its higher transmissibility.
“And we are treating over 1,300 people who are in hospital with Covid.”
He said the government would look to treat more positive cases at home using anti-viral drugs in order to ease pressure on hospitals.
He also repeated advice that unless very urgent or life-threatening, patients should not attend A&E without first calling NHS24 on 111.