Humza Yousaf said the codes would enable people without smartphones to show they had been vaccinated and can be downloaded from the NHS Inform website.
They can also be posted to people who request them by phone as of Friday.
Vaccinated children over 12 will only be able to request a copy of their vaccination status by phoning the Covid-19 Status Helpline.
The news comes as Nicola Sturgeon announced on Wednesday plans for vaccine passports to be required for entry to nightclubs and many large events in Scotland from the end of September.
Some clubs have already introduced the need for proof of vaccination.
The requirement, which will go before the Scottish parliament next week, would apply to indoor and outdoor events.
The First Minister said the move was necessary in order to help tackle the recent rise in the number of covid cases.