This change permits more people to meet outdoors and inside pubs and restaurants.
It was hoped that most of the mainland would join some island communities in Level 0 this summer, but with rising coronavirus cases, there are fears that the government’s roadmap out of lockdown will be thrown off-course.
Now Ms Sturgeon has confirmed it is “likely” that more parts of the country will not enter Level 0 this month.
So, when might areas move down to the lowest level of restrictions - and what does “nearly normal” entail?
Here is everything you need to know.
What areas of Scotland are in Level 0?
Some areas of the country have already moved down to Level 0.
From midnight on Saturday 5 June, Shetland, Orkney and the Western Isles moved from Level 1 into the lowest level of Covid rules.
However, that was excluding Skye, which moved into Level 1.
The full list is: all Highland islands (except Skye), Orkney, Shetland, Na h-Eileanan Siar (Outer Hebrides) and Argyll and Bute islands of Coll, Colonsay, Erraid, Gometra, Iona, Islay, Jura, Mull, Oronsay, Tiree and Ulva.
When could the rest of Scotland move to Level 0?
The First Minister confirmed in her update to Holyrood on Tuesday (15 June) that it is unlikely any further lockdown easing will take place at the end of the month.
A solid decision will be taken and announced next week, she said, but she warned MSPs that current Covid restrictions will likely be kept in place for a further three weeks from 28 June.
That means it is possible that more parts of the country will not move into Level 0 then, as was previously hoped.
Scots could now be looking to 19 July for any more easing of restrictions.
Ms Sturgeon said the extra time would be used to aid the vaccine rollout, giving second doses to as many people as possible and allowing vaccination to get ahead of the virus.
"Doing that will give us the best chance, later in July, of getting back on track and restoring the much greater normality that we all crave," she said.
A decision not to go ahead with the major changes would mirror the announcement made by Prime Minister Boris Johnson yesterday (Monday 14 June), as he extended England’s restrictions by another four weeks, pushing so-called “Freedom Day” back to 19 July.
The rapid spread of the Delta variant first identified in India has led the Scottish Government to adopt a further cautious approach.
However, the First Minister said the government would be considering if any minor changes were able to take place, acknowledging "perceived anomalies" in restrictions.
What rules do we need to follow in Level 0?
This level is described as “nearly normal”, except from physical distancing rules, limits on numbers socialising and some hospitality restrictions.
In Level 0, 10 adults from four households are able to meet in cafes and pubs, while 15 adults from 15 households can meet outdoors.
Ceremonies, like weddings and funerals, can be attended by 200 people.
And the capacity for seated indoor events goes up to 400 people, while outside this is 1,000 at standing events and 2,000 at seated or open space events.
Night-time venues and adult entertainment venues will remain closed even in Level 0 except for use in “limited circumstances”.
And people will still be asked to work from home where they can, although there will be a limited phased return to offices.
All plans are subject to review and rely on the continued suppression of the virus and the success of the vaccinations rollout.