Detectives from Melbourne Sexual Offence and Child Abuse Investigation Team are investigating a report of sexual activity in front of a child in Richmond on 1 October, Victoria Police say.
Detectives have been told an unknown man sat beside a mother and her 14-year-old daughter at a sporting family day on Punt Road in Richmond about 10.50am.
While seated beside them, he faced them before exposing himself and masturbating.
The man is described as aged in his 60s, tall with a pale complexion and had moles on his legs.
He was wearing a navy jumper, white cap, navy shorts with a white stripe on the side, trekking style runners and blue socks with green and black print.
He was wearing a black backpack with shoestring style straps and was carrying a Richmond Tigers scarf.
Investigators have released a facial composite and a profile image of a man they believe may be able to assist with their enquiries.
Anyone with information is urged to contact Crime Stoppers.