Those who have been vaccinated can download a letter from the NHS Inform patient website, or request a letter from the Covid Status Helpline if they are not online.
The status certificate provides a record of the coronavirus vaccinations an individual has received.
BBC Scotland reported that it was able to download a certificate and edit it to include a false name and the address of the BBC’s Glasgow headquarters.
The broadcaster said it discovered that personal details can be altered using popular computer software programmes.
A Scottish Government spokesperson said: “We are working to resolve this issue.
“This is an interim solution and records of vaccination status will be replaced by digital Covid Status Certificates in the summer, which will include vaccination and testing data to be used for outbound international travel.
“The measures are intended to ease the burden on the NHS by removing the need for people to ask their GP for a status record.”
The Scottish Conservatives said the problem must be sorted out immediately.
Annie Wells, Scottish Conservatives shadow health secretary, said: “It’s extremely concerning that this security flaw has been uncovered at a time when people are looking for clarity from the Scottish Government around international travel.
“Instead, their safety is being put at risk by yet another glitch from the SNP Government’s rollout programme, this time on vaccine certifications.
“Vaccinations are our route back to normality and the Scottish Government has a duty to ensure this is done safely and efficiently.
“This security flaw must be rectified instantly – we can’t run the risk of a two-tier vaccine system.”
The Scottish Government said that only those travelling to a country where proof of vaccination is needed as an entry requirement should request a letter.