The finance minister has ordered an immediate review of data protection systems in the NI civil service after the loss of two government discs.
The discs contain details of 237,000 Northern Ireland claimants
The discs contain the personal details of people who receive child benefit including almost a quarter of a million families in Northern Ireland.
The Information Commissioner's Office in NI received two days worth of calls in two hours about the matter.
Banks are advising customers to watch accounts for signs of fraud.
Mr Robinson said: "Given the gravity of yesterday's events and the need to reassure the public and indeed our own staff that proper systems of information management and control are in place and functioning properly, I have instigated an immediate four-week review.
"The review will examine in close detail the effectiveness of personal data security systems across the Northern Ireland Departments in order to provide reassurance to the public that their personal information is being protected properly."
The child benefit data includes names, ages, bank and address details.
The discs were lost in the internal post between HM Revenue and Customs and the audit office.
In total, the discs contain information on 25m adults and children. Officials said child benefit payments would not affected.
Northern Ireland's Information Commissioner Marie Anderson said her office had been very busy.
"I've had to move staff from other activities... onto the advice line," she said.
"People want to know what they should do now. They're worried about if they should contact their bank and we are advising them that they should check their bank statements.
"If they see any transactions that they don't recognise contact the bank immediately."
Chancellor Alastair Darling said banks were monitoring all 7.25m bank accounts whose details were on the discs.
Mr Darling said that anyone who lost money as a result of any misuse of the data would be covered for losses under the banking code.
The Revenue and Customs service has set up a child benefit helpline on 0845 302 1444 for customers who want more details.