A “vaccination status letter” can be downloaded online from the NHS Inform patient portal, or requested in the post via a Freephone Covid Status Helpline.
The service is only for those planning to travel to a country where proof of vaccination status is required.
There are currently no countries requiring this for travellers from Scotland, but the situation may change quickly, the Scottish Government said.
The measure is aimed at speeding up the process and reducing the burden on GP practices being asked for vaccination proof.
In future, digital ‘Covid Status Certificates’ will be used instead of these letters. These will also include information about testing.
Chief medical officer Dr Gregor Smith said people should be cautious and only travel if necessary.
"Given the risk of returning with infection, and especially of introducing new variants of the virus, we continue to be highly cautious about international travel,” he said.
"Everyone should continue to limit their travel abroad and while I understand the need for some people who want to reunite with family, when it comes to holidays, my advice continues to be play it safe and staycation this summer.
“For those that do need it, this new service will provide people with a record of their vaccination status for outbound international travel.
“They should only access their record if they are planning to travel within 21 days and it is a requirement of their destination.”
The system differs from the one being used in England where an NHS app – separate from its contact tracing app – can show vaccine status if enabled by a GP.
Scottish Labour deputy leader and health spokeswoman Jackie Baillie said: “I welcome the news that the Scottish Government is pro-actively looking to implement a vaccine certificate scheme.
“It is important that Scottish ministers continue to urge caution around foreign travel whilst we are in the midst of the pandemic.
“The Scottish Government should also make it clear that the vaccine certificate is for foreign travel only, and that they are not needed for domestic travel across Britain.”
Scottish Liberal Democrat leader Willie Rennie said: “Whilst we have no major issues with the limited use of such vaccine passports for international travel when other countries require it, Liberal Democrats are very concerned about the possible widespread use for domestic purposes.
“It would be a major step for the government to require medical treatment for access to everyday services. A vaccine ID card could also be the first step to a full ID card, which we oppose.”
Covid status certificates have been trialled in England since mid last month.
The UK Government previously said such a scheme could have an important role to play both domestically and internationally and was "likely to become a feature of our lives until the pandemic recedes".
Prime Minister Boris Johnson has consistently said vaccine passports would have a role to play when international travel resumed.