Halima Nassif is alleged to have left the boy in the care of an unregistered family member to go to another job when he sustained a severe head injury.
The Care Inspectorate has imposed an emergency condition preventing her from childminding while police investigate the incident at an address in Limefield, Edinburgh, on February 8.
The child was taken to the Royal Hospital for Sick Children where he remains in a stable condition.
A letter from the Care Inspectorate to Ms Nassif states: "The reasons for this decision are that the Care Inspectorate has been made aware of an allegation that on Saturday, 8 February, you knowingly left a minded child in the care of an unregistered member of your family.
"During your absence from your childminding service and whilst in the sole care of your unregistered family member, the minded child sustained a head injury.
"The Care Inspectorate has reason to believe that you left the minded child in order to pursue other employment which on occasion, takes place during the hours of operation of your childminding service.
"The Care Inspectorate also has reason to believe that your 'other employment' is ongoing and can therefore not be satisfied that you would not leave minded children in the care of a person or persons who are not fit to provide a care service in the future."
The letter said that without the emergency condition "there is a serious risk to the life, health or well-being of persons attending the service".
Ms Nassif has said she intends to cancel her registration as a childminder, according to the inspectorate.
A spokesman said: "We imposed an emergency condition notice on this childminder's registration, which prevents her from childminding pending the outcome of police inquiries.
"The individual concerned has now notified us of her intention to cancel her registration.
"We are working closely with the police. Anyone with concerns about any care service can contact us on 0845 6009527."
Police Scotland said inquiries into the incident are continuing.