The SNP leader, who is 50-years-old, urged others to get the vaccine when they are offered it.
Regulator says young people will be offered the Pfizer or Moderna vaccination instead.
World Health Organisation and European Medicines Agency say there is no evidence the jab causes blood clots.
UK’s Medicines and Healthcare products Regulatory Agency says evidence does not suggest vaccine is the cause of blood clots.
Researchers say that the first dose of the Oxford/AstraZeneca jab may reduce transmission by 67%.
Scotland has an allocation of 533,640 doses of the Oxford/AstraZeneca vaccine for the month of January.