Four cases of the newly-discovered strain are in the Lanarkshire area and two have been identified in the Greater Glasgow and Clyde area.
It understood that ‘some degree of community transmission’ took place as some patients with the new virus in Scotland do not have any travel history.
Out of those infected, there is no evidence of serious illness at the moment.
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It comes as Nicola Sturgeon is expected to urge Scots to ‘redouble efforts’ in the fight against covid to ‘maximise’ chance of having a ‘more normal Christmas’ in her speech to the SNP conference on Monday at 10.30am.
She will warn Scotland faces “big and very real challenges ahead over the winter months”.
The Scottish Government has said that Public Health Scotland and local health protection teams are supporting and contact tracing is being undertaken to establish the origin of the virus and any individuals they have come into contact with in recent weeks.
Humza Yousaf, health secretary, said enhanced contact tracing is being introduced to redouble efforts in tackling the virus.
The heath secretary said: “This will be a worrying time for the six people now identified as having the new variant.
"All will receive expert help and support and Public Health Scotland will undertake enhanced contact tracing in all cases. This will help establish the origin of the virus and any further individuals they have come into contact with in recent weeks.
“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. Until more is known we must be cautious and do everything we can to minimise the risk of spreading infection.”
Speaking on BBC’s Good Morning Scotland on Monday, John Swinney, deputy first minister, told the programme that some of the cases do not involve ‘travel history’ to South Africa.
Mr Swinney said: "What that tells us is 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.
"It is as yet unclear whether the Omicron strain gives rise to serious illness but it certainly does look that it is more transmissible than the Delta variant.”
Mr Yousaf said that the Scottish Government is 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.
He added: “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 are also adopting the expanded red list of countries identified by the UK Government. This will also be kept under review.”