The decision comes after Nicola Sturgeon said last week that Cabinet was considering an expansion to the programme, with cinemas, theatres and other hospitality venues in scope.
But this expansion will not yet take place, the First Minister confirmed to MSPs on Tuesday.
The scheme will, however, be altered to include proof of a negative lateral flow test in the past 48 hours, which will come into effect from December 6. NHS text notifications following PCR or self-reported lateral flow tests will be accepted.
Venues already affected by the scheme, including nightclubs and large-scale indoor and outdoor events, will continue to require vaccine passport checks for at least a further three weeks.
All other Covid-related restrictions in place will also remain, including the requirement to wear face coverings.
Business representatives welcomed the decision that no further venues will need certification.
The Scottish Licensed Trade Association (SLTA) said pubs, bars and restaurants had been brought “back from the brink” by the decision.
SLTA managing director Colin Wilkinson said: “Indications were that a widening of the vaccine certification scheme to pubs, bars, restaurants would be brought in, forcing many premises into closure.
"This reprieve will be a great relief to the many businesses that feared a similar negative impact would be mirrored in the wider licensed hospitality sector, particularly at this crucial time of the year for the industry.”
Paul Togneri, from the Scottish Beer and Pub Association, said venues had “breathed a great sigh of relief”.
“We have been in close dialogue with ministers, officials and public health discussing the potential economic impact and the operational practicalities extending the scheme would have entailed,” he said.
“We are thankful to them for listening to us and, in doing so, may have averted an economic disaster for many businesses this Christmas.”
Marc Crothall, chief executive of the Scottish Tourism Alliance, said the move would have impacted the tourism sector.
He said: “The proposal to extend vaccine certification to hospitality was, in our view, harmful to the sector, the wider tourism economy across all areas of Scotland and would have effectively stalled what is already a long and challenging road to recovery for one of the worst hit industries.”
With the festive period key for firms trying to recoup money lost in earlier lockdowns, Mr Crothall said “many businesses will feel a sense of overwhelming relief that they will be able to trade as planned”.
However, public health expert Professor Devi Sridhar said she believed the government had made the wrong decision.
Prof Sridhar, who has previously recommended the scheme be extended to further venues, wrote on Twitter: “I personally think it would be better to go further with certification now. We’ve learned that waiting & watching just makes the problem worse. And we’re heading into Dec-Feb, hardest months for the NHS.”
Professor Rowland Kao, chair of veterinary epidemiology and data science at Edinburgh University, said the decision not to roll out to further venues was likely based on several factors.
These may include how well the population could tolerate another full lockdown if protective measures are not put in place now, and the protests at Covid pass schemes in Europe, he said.
Existing measures of Covid in Scotland are also not as bad as they could be, he added, with the situation “stable and heading in the right direction”.
“Cases are going down or stabilised,” he said.
“Hospitalisations at the moment appear to be, depending on where you are, going down or stable.
“All the metrics are pretty good for the moment, and so they may have simply decided that for the moment, the risk of things going up again, or that flu will actually cause things to get worse, isn't high enough.”
Prof Kao said increased uptake of first round and booster vaccinations may also be a contributing factor.
“Around a month ago the worry was that you were starting to see vaccinated individuals starting to go to hospital in increasing numbers,” he said.
“But I think what's happening now is the boosters are showing evidence of helping.”
Ms Sturgeon told MSPs the decision was a “finely balanced” one.
She said: “Cabinet ... considered the possible extension of the scheme to a much wider range of premises, including indoor theatres, cinemas and hospitality venues.
“This was a very finely balanced decision. However, I can confirm that at this stage we have decided not to extend the scope of the scheme.
“We have taken account of the fact that – although our situation is precarious – cases are currently stable and indeed slightly declining, and we have considered the inevitable impact vaccine certification has on the operation of businesses; and concluded that, at this stage, extension would not be proportionate.
"We were also mindful of the need over the coming weeks of getting across the message that it is important to be vaccinated and tested ahead of socialising in any setting, including in homes and shopping centres, for example, not just in those that might be covered by a certification scheme.”
The decision comes after vaccine passports were rolled out to cinemas, theatres and concert halls in Wales from November 15.
The Welsh scheme also allows for proof of a negative lateral flow test.
Opposition MSPs welcomed the inclusion of negative tests in Scotland’s scheme and the decision not to roll out more widely.
Scottish Conservative health spokesman Dr Sandesh Gulhane accused the Scottish Government of “making it up as they go along” after the uncertainty of the past fortnight.
“It is a relief that the vaccine passport scheme is not being extended,” he said.
"But the uncertainty that this government has left hanging over businesses for the past two weeks has been unnecessary and unacceptable.
“The Scottish Government released their so-called ‘evidence’ paper on Friday, yet in almost 70 pages were unable to offer proof of the scheme’s effectiveness. It seems more and more like they’re making it up as they go along.”
Scottish Labour said the government had previously focused on the “wrong priority” of vaccination rather than testing.
Party leader Anas Sarwar said: “I welcome the government’s U-turn today, but it is clear that the First Minister has wasted months ignoring experts and the evidence.”
The Liberal Democrats, who have opposed vaccine passports from the beginning, continue to do so.
Leader Alex Cole-Hamilton said: “Lateral flow tests are superior to vaccine passports because they actually show who is sick and who is well.
“The government has finally accepted that today, but only after causing panic amongst businesses.”