The charity said it was appalled at Friday’s break in but moved to reassure the public that patients’ confidential files had not been stolen.
Councillor Duffy said: “This is absolutely a disgraceful incident.
“I was shocked to hear that the Men’s Action Network office on Patrick Street had been burgled and vital equipment stolen.
“I know of the great work that they carry out across the city and hope that they can get their offices back up and running again as soon as possible.
“If anyone has any information on this incident or finds any equipment in the laneways in the surrounding area, they should contact the PSNI.”