The Roodepoort Department of Home Affairs office won't be opening its doors on Monday, following a break-in on Sunday.
"During the burglary, which took place yesterday, computers were stolen," the department's David Hlabane said in a statement.
"The department is unable, at this stage, to say when services will resume. However, the intention is to resume service as soon as possible," he said.
"Clients who require services urgently, should visit any nearest office for help."
The matter has been reported to the police.
The department urged South Africans to be patient as it resolved an issue that was "beyond their control".
"It will do all in its power to ensure a speedy resumption of services to minimise the impact and inconvenience caused to the people who rely on its services," Hlabane said.