Thieves broke into Middlesbrough Council's teaching and learning centre on 6 January.
The laptops were used by child workers and contained case files on children and their families.
The council said after consulting police they would contact selected individuals most at risk.
The information was password protected with some encryption and did not include any personal financial information.
Minimal risk
It has also emerged another laptop had been stolen before Christmas but only contained a limited number of names and addresses of council service users.
Cleveland Police are investigating both incidents and are appealing for witnesses.
Gill Rollings, director of children, families and learning said: "We believe that the nature of the information means that the possibility of risk to anyone is minimal.
"Indications are that the thieves were seeking the equipment rather than any information."
Following a review, the council is stepping up password, encryption and building security.
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