Police in Melbourne, Australia, have shot dead a man who had taken a woman hostage in the Brighton area of the city, reports said.

Three officers were injured after they stormed an apartment block in Melbourne's Bayside suburbs during the siege, said a report in ABC website.

The stand-off began in the afternoon when emergency services responded to reports of an explosion in Bay Street. A man's body was found in the foyer of an apartment block. Police believe he had been shot.

Specialist police then attempted to negotiate with another man who was holding a woman hostage, the report said.

"A man has been shot dead by police in the Bay Street apartment complex shortly before 6:00," police said following the siege. "Police have safely rescued a woman who was being held against her will in the apartment block."

Police are investigating whether the incident is terrorism related.