An Australian man serving 35 years in jail for the rape and murder of Irish woman Jill Meagher has been injured during a prison fight.

Adrian Ernest Bayley pleaded guilty and was sentenced in 2013 for the rape and murder of Ms Meagher in a Melbourne suburb the previous September.

Ms Meagher (29) was walking home from a pub in the town of Brunswick in the early hours of Saturday September 22nd 2012, when she disappeared on Sydney Road.

Her body was discovered six days later buried in an area 50 kilometres from Brunswick.

Jill Meagher | File photo

Australia's Herald Sun reports that Bayley was involved in a brawl with fellow prisoner Steven James Hunter.

It said Bayley "punched on for more than three minutes at a protection unit in Barwon Prison."

It added that Hunter was treated in hospital for a head injury, but has since returned to the maximum-security prison.

It is not known what prompted the fight.

A Corrections Victoria spokesman said: "Corrections Victoria takes all assaults very seriously, and refers all allegations of criminal activity to Victoria Police for investigation".

Hunter and Bayley are kept separate from the general jail population because their safety is at risk from other inmates.

Hunter is serving life without parole for the murder of 22-year-old Sarah Cafferkey in November 2012.

In 1986, he was also sentenced to a maximum of 16 years' jail for stabbing 18-year-old schoolgirl Jacqueline Cecilia Mathews to death.

Bayley will not be eligible for parole until at least 2058.