The University has closed two floors in the building where all seven people worked, and has set up a helpline for anyone with questions or concerns.
The union's Victorian secretary, Matthew McGowan, says while it's not yet known whether there is a common link between the cases, the telecommunications towers on the building's roof should be the focus of the investigation.
"It does seem like an extraordinary coincidence that there is a mobile phone tower immediately on top of this building and five of the seven people who have been affected have worked for a long period of time on that floor."
He says; "It's a very strange coincidence. However, we don't know definitively, but we want these questions looked into and we want them tracked down fairly comprehensively."