Two of the infections were detected in the Glasgow and Clyde region and the other four were found in Lanarkshire.
Public Health Scotland and local authorities are now tracing the contacts of the people infected, the government said in a statement.
Humza Yousef, Scotland’s health secretary, said in the statement: “There is still much to learn about the omicron variant. Questions remain about its severity, transmissibility and response to treatments or vaccines and scientists are working at pace to provide additional information.
“We have already taken steps and are aligning with the new border restrictions being introduced by the UK government which will require fully vaccinated arrivals to take a PCR test within two days of arrival and to self-isolate until a negative result is received.
“These measures will be introduced as soon as possible and kept under constant review. However, we reserve the right to go further if necessary.
“We must now redouble our efforts to follow the basic rules that have served us well throughout the pandemic.
“If you have symptoms, self-isolate and take a test and if contacted by Test and Protect or public health teams please co-operate.”
Mr Yousaf also urged people to get their booster jab when invited.
John Swinney, Scotland’s deputy first minister, said “some” of the new infections were not linked to foreign travel.
He told Good Morning Scotland: “There must be a degree of community transmission of this particular strain of the virus in the absence of direct travel connection for some of the cases in the southern African area.
“So that obviously opens up further challenges for us in terms of interrupting the spread of this particular strain of the virus and that will be the focus of the contact tracing operation that is under way already.”
Omicron, or B.1.1529, was first recorded in Botswana in southern Africa in mid-November. It has an unusually high number of mutations in its spike proteins – 32 – compared to the original Covid-19 strain.
The UK has now recorded a total of nine omicron infections. However, in its region of origin the variant is feared to be the source of most new infections and to be supplanting delta as the most prominent strain, suggesting more cases may soon come to light in Britain.
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