According to Police, the children aged six-months and three-years were reported as being left without the care of their mother for 4 days.
The mother was seen leaving her children for a social outing.
In the early hours of Tuesday last week, the situation was reported to Nauru Police Force, as the mother had still not returned home.
The case was referred to the Domestic Violence Unit, and the mother has since been apprehended.
The children are safe and well.
Under Nauru's Crimes Act 2016, Section 94, neglecting a child is a crime attracting 10 years in jail.
The Nauru Police Force said it is very concerned, and will not tolerate this behaviour, but rather, will put offenders to task for it.
Report child neglect with confidence on 7-9014 or 7-9024, or 110.