The nine laptops were used by staff in Middlesbrough Council's Children, Families and Learning Department, and went missing after a break-in.
The machines could contain private information on up to 63 vulnerable youngsters and their families, reports the paper.
The computers were used by educational psychologists and social workers. The council said the data goes back up to 18 months. None of it contained financial details of families.
The computers were taken from locked drawers in a locked room in a locked building, the council told the paper.
The building had been a target for burglars before. All the laptops were password protected with "some encryption", the council told the paper.