A total of 9,360 new positive cases have been confirmed in the last 24 hours, according to the latest Scottish Government data released on Tuesday.
The day before, 10,562 cases were recorded, with 11,030 cases on December 26.
These daily figures are the highest Scotland has seen since the first coronavirus case was recorded in the country in March 2020.
While the data covers tests reported in the preceding 24-hour period, a lag in reporting means that the majority of these cases will relate to tests done before the Christmas break.
Some people in Scotland are currently waiting up to four days for a PCR test result, which should normally take only 24 hours.
With the current longer turnaround time for test results, this could mean the actual number of positive Covid-19 cases is higher.
"These figures serve to underline the importance of people continuing to get 'boosted by the bells' and following the guidance to help slow the spread of Covid while we complete the accelerated booster programme," she said.
"I know it is hard, but it is really important people continue to comply with the guidance over the new year period.
"Even if the rate of hospitalisation associated with it is lower than past strains of the virus, case numbers this high will still put an inevitable further strain on the NHS, and create significant levels of disruption due to sickness absence across the economy and critical services."
She again urged people to limit their in-person socialising over the festive period, limiting contact "as much as possible" and to keep any essential indoor gatherings to a maximum of three households.
Earlier on Tuesday, Scotland's national clinical director Professor Jason Leitch said the waiting time for PCR Covid test results in Scotland should have returned to normal.
Speaking on BBC's Good Morning Scotland, he said: "My understanding was, yesterday (Monday), speaking to test and protect leaders, that the backlog was cleared and they were back to somewhere between 24 and 36 hours for pretty much all the tests.
Asked why people had had to wait such a long time for test results, Prof Leitch said it had just been scale due to many people testing before the Christmas break.
When asked about the number of Omicron hospital admissions, Prof Leitch said they are not rising at the rate they rose with Delta.
While he said it was important to not overreact to the current record case numbers, he added: "Nor should we underreact, because if you have four times as many cases, even with a quarter of the severity, you are going to end up with the same number of people needing ventilated and the same number dying."
A full update on cases is expected on Wednesday when the First Minister is due to give a Covid statement in Parliament.
Provisional Scottish Government data on case numbers are as follows:
December 25: 8,252 cases
December 26: 11,030 cases
December 27: 10,562 cases
December 28: 9,360 cases