Authorities have said the nine cases across Lanarkshire area and Greater Glasgow and Clyde (NHSGGC) identified earlier in the week were connected to an event on November 20.
Public Health Scotland recorded an additional confirmed case of the Omicron variant of Covid-19 on Wednesday in the NHSGGC area.
All close contacts of suspected Omicron cases will be advised to self-isolate for 10 days, regardless of their vaccination status.
A Scottish Government spokesman said: “The individual affected is in the NHS Greater Glasgow and Clyde health board area and while there is no direct link with the event on the 20th November which connected the previous nine cases, investigations are ongoing.
“As First Minister Nicola Sturgeon told parliament on Tuesday, it was already suspected that some degree of community transmission of this variant was taking place in Scotland.
“However, there is no indication as yet that transmission of the new variant is either sustained or widespread.
“Public Health Scotland is working hard to identify any and all cases of Omicron in Scotland as quickly as possible.
“This enhanced surveillance gives us the best possible chance of identifying cases quickly, breaking transmission chains and containing spread while we learn more about this variant.”
The Scottish Government said that vaccination is the “most important line of defence” and also urged people to comply “rigorously” with all the protections currently in place to stem transmission.
First Minister Ms Sturgeon has said she is not asking people to put Christmas plans on hold at the moment following the emergence of the Omicron variant but she urged people to take a lateral flow test before mixing with other households.
Booster vaccinations are being extended to all those aged 18 and the interval between the second and third dose is being cut from six to three months after a recommendation from the UK’s Joint Committee on Vaccination and Immunisation.
A Government minister has urged people to be “sensible” this Christmas in order to avoid further restrictions in the face of the Omicron variant threat.