Spokesman Castro Ngobese said it appeared to have happened on Sunday night.
“We opened a case with the SA Police Service on Monday,” he said in a statement.
No arrests had been made. Ngobese said the burglars tried to set the office alight but failed to do so.
“A number of cellphones and spare keys were stolen,” he said.
This was not the first attempt to destroy the union’s offices.
“This follows a long list of similar acts of burglary and vandalism that have occurred at our head offices last year,” Ngobese said.
The union’s offices in Newtown, Johannesburg, were burgled in May and again in September 2013. No arrests had been made following either of the break-ins.
Security at both the Bellville and Johannesburg offices had since been tightened.