Police said the unknown man approached a 33-year-old Werribee man at a licensed premises in Southbank on Saturday, November 30 and unsuccessfully tried to snatch the money from his hand.
Investigators were told the man then attempted to hit the man with the axe and missed.
The 33-year-old was not physically injured.
Witnesses said the unknown assailant left the venue.
Police have released CCTV and images of a man who they believe may be able to assist with their enquiries.
The man depicted was wearing what police described as a “black Post Modern jacket” with a light blue shirt and dark tie.
He was also wearing light blue jeans, a black baseball cap, black shoes and a black bum bag.
He also had a dark canvas shopping trolley.
Police are investigating whether the attempted armed robbery is related to another incident which happened in Hoppers Crossing on Sunday, December 1.
It is understood a staff member offered to assist a man in a shop before the man took out a hammer at about 11.20am.
Police were told the stranger threatened the 47-year-old man then stole the items and left the store.
The man was not physically injured.