Police have shot and killed a man following a tense hostage situation at a Melbourne unit complex.

The man was holed up inside a Bay Street, Brighton apartment building and had taken a woman hostage.

He had also shot and killed another man in the foyer of the complex about 4pm.

Police have resolved a hostage situation in Brighton shooting a man dead and rescuing a woman being held against her will. — Victoria Police (@VictoriaPolice) June 5, 2017

Police shot the hostage taker shortly before 6pm and rescued the woman.

Three police officers sustained non-life threatening injuries during the altercation and two have been taken to hospital for treatment.

Victoria Police say they are investigating whether the incident was terror-related.