The case is connected to an individual who few to Scotland from Rio de Janeiro via Paris and arrived in Edinburgh on February 19.
First Minister Nicola Sturgeon said the passenger had followed the rules around hotel quarantine and added there was no sign of any onward community transmission, with contact tracing ongoing for other individuals on the flight.
The flight from Paris to Edinburgh included 22 passengers, with 11 passengers exempt from quarantining in hotels and instead allowed to self-isolate at home.
The rest of the flight went directly into hotel quarantine.
Negative test results for 13 individuals were recorded on day two and day eight of their isolation period, with the National Contact Tracing Centre following up with the other eight passengers.
No further positive cases of the Brazilian variant linked to this case have been detected in Scotland.
Ms Sturgeon said: “A possible – although still unconfirmed – further case of the P1 variant in Scotland has now been identified. It involves an individual who travelled to Scotland from Rio de Janeiro, via Paris, and arrived on February 19.
"The individual followed the procedures for managed self-isolation and we currently have no reason to believe that this case presents any risk to the wider community. However, we are of course continuing to undertake all necessary follow-up work.”
It is the second time a variant of concern has been detected in Scotland following three cases identified in the north east of Scotland in late February.
That case had arrived via a flight from Heathrow to Aberdeen on January 29, with genomic sequencing identifying it as a variant of concern on February 27.
The P1 “Brazilian” variant is a descendent of B.1.1.28 and was first detected in Japan, but is most closely associated with the second wave epidemic in Manaus, Brazil.
This variant has been designated ‘of concern’ as it shares some important mutations with the variant first identified in South Africa. It is possible this variant may respond less well to current vaccines.
This effect on vaccines is still highly uncertain, with clinical and trial data awaited for a clearer picture.