Ms Sturgeon said local authorities would receive £12.6m, (€14m), to provide the service to about 175,000 pupils.
That number has risen by 53,000 since the start of the pandemic due to the impact it has had on family incomes.
Meals are currently distributed in schools that are still open or through direct cash or voucher payments.
The funding will see the scheme extended from the end of June through to the start of the new term in August.
During her daily briefing Ms.Sturgeon said: “We know families are under considerable financial pressure just now and free school meals are a vital help to many but they are also really important to the health and wellbeing of children.”
The funding was announced shortly before the UK government confirmed the school meal voucher scheme will be extended in England.
This followed a campaign by footballer Marcus Rashford, which was praised by Ms.Sturgeon.