Investigators were told the man sat outside of the woman’s home on Grey Street in St Kilda just after 2pm on February 10 and refused to leave.
The pair started to argue and the woman allegedly hit the man in the head.
The man then allegedly retaliated by striking the woman in the head twice with the toolbox and punching her multiple times in the face before he left the property.
The 55-year-old woman was taken to hospital with a concussion and a large laceration at the back of her head.
Police said the man is perceived to be of Middle Eastern appearance, around 30 years old, with a dark beard and a tattoo of an owl on his left calf.
He was wearing a black cap, yellow high-vis t-shirt, khaki shorts and black shoes.
Police have released an image of a man today they believe can assist with their investigation as they continue to appeal for witnesses and CCTV.