The computer was stolen during a break-in between during the weekend of November 30th to December 3rd, Politiken reports.
Information stored on the machine includes personal registration numbers, age, gender, address and marital status.
In some cases, details of social welfare payments and housing as well as membership of the Church of Denmark are also listed.
Gladsaxe Municipality informed affected residents of the issue on Monday.
Personal information is normally protected, including from incidences of theft, according to the council.
“But in this case, one of the (stolen) computers contained a spreadsheet with confidential information which, due to human error, was temporarily saved locally on the computer,” the municipality wrote.
It is unclear whether people living in other municipalities may also have been affected, given that the data was for the purpose of checking accounts between Gladsaxe and other areas.
The municipality has reported the incident to the Danish Data Protection Agency (Datatilsynet) and to the police, but risks a fine over the incident due to GDPR rules.
Municipal director Bo Rasmussen expressed his apologies over the theft and said it was difficult to prevent human error.
“But we have, in the last few months, made a huge effort to inform our managers and staff on how to deal with sensitive information in a secure way according to data protection rules. But this happened nevertheless,” Rasmussen said to Politiken.
“That’s not good enough,” he said.
The director added that he hoped the theft was targeted at the hardware rather than the data, in which case the hard disk containing the confidential information is likely to have been wiped.