Human Resources and Skills Development Canada notified the privacy commissioner's office on Dec. 21 that the data had been lost.
About 5,000 people are believed to be affected and are receiving letters notifying them of the privacy breach and steps they need to take to protect their information.
About 60 people have already called an information line at the privacy commissioner's office expressing concern about the incident and complaints have already been filed.
"It's too early to say whether or not these will turn into official, full, investigations," said Anne-Marie Hayden, a spokeswoman for the privacy commissioner.
"We'd have to look at what we receive first and determine next steps from there.
But the commissioner's office is working with HRSDC to try to figure out what happened.
The department handles a variety of files including pensions, old age security, employment insurance and childcare tax credits.
Each year, federal departments are required to report on how well they comply with privacy legislation.
In the 2010-11 report — the most recent one posted on HRSDC's website — the department noted that it had been the subject of three complaints regarding how it handled personal information.