Recent exponential growth in Covid case numbers have increased the burden on hospitals, primary care and care homes, a spokesperson said.
In a bulletin circulated to staff, officials said the planned response would include declaring a major incident, which could happen as soon as next week.
It comes after critical incidents have been declared in several NHS trusts in England this week.
Health boards across Scotland have warned of unsustainable pressures, with NHS Greater Glasgow and Clyde warning on Thursday that staff were “struggling to cope”.
Additional military personnel began inductions in NHS Grampian, Lanarkshire and Ayrshire and Arran on Friday in a bid to relieve pressure.
"We have seen exponential growth of case numbers in Grampian and Scotland in the past fortnight,” a spokesperson for NHS Grampian said.
"Based on our modelling data, we anticipate a continued and significant growth in the levels of the disease placing even more significant pressure on care homes, primary care teams, community teams and hospitals.
"Our planned response will include a declaration of a major incident when a number of key trigger points are reached. This decision will be taken by our Strategic and Tactical Commanders based on the system pressures, number of Covid patients in hospital and levels of staff sickness from Covid.
"Looking at our local data, these triggers could be met as early as the end of next week.
"We are currently planning what this means for staff, patients and services in Grampian.
"Thank you to the public and, of course, our incredible staff for everything you are doing during the most challenging of times. Our collective actions make all the difference."