There will also be a phased return of secondary school pupils from the same date.
The First Minister’s lockdown review on Tuesday 2 March focused on education and enabling children to go back to classrooms.
Addressing the Scottish Parliament, Ms Sturgeon announced that the next phase of reopening education, part of the roadmap out of lockdown, would go ahead as planned.
The SNP leader also said that ministers were “considering if it might be possible to accelerate the exit from lockdown in any way”.
Here is everything Ms Sturgeon announced today.
What did the First Minister say?
Ms Sturgeon said there had been “good progress” in suppressing the virus, as cases and hospital admissions in Scotland were still declining.
She also shared her hope that this would be “the last lockdown” for the country.
However, the SNP leader made clear that care needed to be taken when relaxing restrictions due to the more transmissible UK variant of coronavirus, along with the P1 Brazil variant which poses a “significant risk”.
Ms Sturgeon said she hopes to be able to confirm further changes to the current Level 4 lockdown restrictions next week.
The government also aims to publish a “firmer timetable” for the reopening of the economy from 26 April soon.
But today’s announcement focused mainly on the return of schools.
When do more school pupils return?
The first phase of the First Minister’s roadmap began on Monday 22 February, when Scotland’s youngest pupils, as well as limited numbers of senior pupils, returned to classrooms.
Ms Sturgeon confirmed today that on 15 March, unless there is new evidence forcing the government to reconsider, phase two of the school return will come into effect.
On that date, primaries four to seven will return on a full time basis.
All primary school children will also be able to return to regulated childcare, including after school and breakfast clubs.
Also from 15 March, there will be a phased return of secondary school pupils.
Ms Sturgeon said she expects that all secondary school pupils will go back to school on a full time basis following the Easter holidays.
But she said she hoped that all secondary school pupils would spend some time in school from 15 March until the break.
Students in the senior phase of secondary school – years four to six – who are taking national qualifications will be prioritised for face-to-face lessons in school.
Education Scotland will publish guidance for local authorities on the phased return of secondary schools during the next week.
Ms Sturgeon said local authorities would have flexibility in how they carry out the phased return.
When secondary pupils do go back, face coverings will need to be worn at all times.
There will also be twice-weekly lateral flow testing for all school staff in primary, secondary and special schools, and for all secondary school pupils in years four, five and six.
Local authorities will be asked to continue to observe the current two metre physical distancing in secondary schools, at least until the Easter holidays.
What could be announced next week?
Next week, the First Minister intends to outline changes to the Level 4 restrictions that could take effect from 15 March.
She said: "We will consider between now and then if the data allows us to bring forward any relaxation of the rules.
"I have always said if we can go further and faster, then we will not hesitate to do so."
That could include a relaxation of the rules around outdoor socialising.
The limit on outdoor mixing between households may be increased to four people from a maximum of two households from 15 March.
But it is possible that restrictions on socialising will not be eased further until the third phase from 5 April.
From then, six people from two households may be permitted to meet outdoors.
However, the “stay at home” restriction is also not expected to be lifted until at least 5 April, when some retailers could start to reopen and communal worship could restart with restricted numbers.
Other restrictions are not expected to ease until the last lockdown phase from 26 April.
A “phased but significant” reopening of the economy is planned for then, with non-essential retail opening back up.
That is when hospitality venues – including bars, restaurants and pubs - may reopen, as well as services like gyms and hairdressers.