The NHS Scotland Covid Status app was made available to download on Apple and Android devices on Thursday afternoon.
From 5am on Friday, people attending large events and nightclubs will need to show proof they have had two doses of vaccine using the app before they are allowed in.
But just hours after the app's launch, comments circulating on social media suggest many users have been unable to register on it.
The Scottish Government said the large volume of people accessing the app at once could be a reason behind the glitch.
A Scottish Government spokesperson said: "Some people may be experiencing issues which are likely to be caused by extremely high initial traffic and a large number of users trying to access the app at once.
"We advise people whose data is not found to try again a couple of hours later."
The launch came on the same day the Night Time Industries Association (NTIA) Scotland lost a legal bid to delay the rollout.
Following consultation with businesses affected, the Scottish Government confirmed a grace period has been agreed until October 18 before the scheme is legally enforced.
The legal requirement for businesses to keep information about certification status confidential and not use it for other purposes comes into effect today.
Speaking about the app's launch, Deputy First Minister John Swinney said: "We know from expert public health analysis that we must do all we can to stem the rise in cases and reduce the pressure on the NHS.
"Vaccine certificates have a role to play as part of a wider package of measures. They add a further layer of protection in certain higher risk settings.
"This is a very limited scheme and we hope this will allow businesses to remain open and prevent any further restrictions as we head into autumn and winter.
"I would encourage people to to download the NHS Scotland Covid Status App and help our drive to keep the virus under control.
"Scotland is not unique in introducing such an approach. Certification schemes are in place across Europe, including Ireland and France, and the Welsh Government is also planning similar measures.