Scotland is expected to move down to level two on May 17, however Jillian Evans the head of health intelligence at NHS Grampian, said Moray would need to "reverse" the rise first.
Ms Evans told BBC Scotland's The Nine programme that the situation in Moray was “very fragile” and "unfamiliar" to residents as they had experienced a very "quiet pandemic" so far.
On May 1, the area in north east Scotland had a rate of 78.3 cases per 100,000 - more than three times the national average (21.9).
Until recent weeks, Moray has seen some of the lowest case rates in mainland Scotland during the course of the outbreak.
The threshold for level three was lowered to 50 cases per 100,000 in March.
However, Moray is currently the only Scottish local authority above this threshold.
Asked whether she would back further restrictions in Moray, Ms Evans replied: "Yes I would actually.
"I would prefer us to consider ways in which we can all keep ourselves safe, whether that needs special measures for Moray.
"We're still in level three at the moment. It's not too late to move along with the rest of Scotland, but that will require people to take regular testing.
"Don't meet up indoors in people's homes and try by and large to follow those guidelines because they are there for a reason."
Ms Evans said the recent rise in infections in Moray was concerning because they were not linked to a "known chain of transmission", with many of the cases also asymptomatic.
"We're not sure if we've seen the numbers peak yet," Ms Evans added.
"I don't think it's too late for us to reverse the situation before the level decisions come in mid-May but it is a very fragile situation at the moment."
Figures published by the Scottish government on Tuesday revealed that there were no covid deaths for the fourth consecutive day.
There are 58 covid patients in hospital and 11 people are being treated in intensive care.