At around 12.45 am, a fire was started at the back door of a house just off the Ormeau Road.
It caused minor damage to the door.
No-one was injured in the incident.
Detective Sergeant Patrick Mullan said: “I would appeal to anyone with any information about this incident to contact CID at Musgrave Police Station on the non emergency number 101.
“Or if someone would prefer to provide information without giving their details they can contact the independent charity crimestoppers and speak to them anonymously on 08000 555 111.”