Two women, aged 25 and 65, have been reported to the procurator fiscal following an investigation at The Hamilton School in Aberdeen.
Police launched an investigation following allegations on a website that was set up about the school.
In a statement, police said: " Police Scotland can confirm that as a result of inquiries at the Hamilton School in Aberdeen, a 65-year-old female and a 25-year-old female will be the subject of a report to the Crown Office and Procurator Fiscal Service.
"As proceedings are now live, there will be no further comment."
The Care Inspectorate said it has informed The Hamilton School that staff who are the subject of a police report must not have contact with the nursery.
It has asked it to appoint a suitably qualified manager.
A Care Inspectorate spokesman said: "As Scotland's care regulator, our top concern is the safety and well-being of children and we know that this will be a difficult and distressing time for families.
"We are working closely with the police and others to safeguard children at the nursery.
"Today, we will offer support and advice to the school to keep disruption to a minimum. Tomorrow, we will start a joint inspection with Education Scotland, which will include assessing the care and learning provided to the children.
"Separately, we continue to investigate a number of complaints about the quality of care. Anyone with concerns can contact our helpline on 0845 600 9527."
Aberdeen City Council said The Hamilton School is privately run and it would be inappropriate for the council to comment on ongoing investigations.
A spokesman for The Hamilton School said: "We will cooperate fully with the police in their inquiries."