First Minister Nicola Sturgeon said 13 council areas would stay in level two due to rising case rates. Most of the country had been due to drop down to level one in the five-tier system from next week.
The BBC reported that the first minister said a "slight slowing down" of the easing of restrictions was needed while vaccination continues - but described it as "a pause, not a step backwards".
Glasgow will enter level two on Saturday, allowing six people from three households to meet up indoors for the first time in many months.
Pubs and restaurants will be able to sell alcohol indoors, and the travel ban between Glasgow and other parts of the country will also be lifted.
Ms Sturgeon said she knew it would be "very disappointing" for the people in these areas, but said: "Taking a cautious approach now - while more people get fully vaccinated - gives us the best chance of staying on the right track overall."