The "heroic" efforts of passers-by to try to save the man have been praised by police who were called to Princes Wharf about 10pm on Monday.
A woman in her 20s, who was with the man and was also pushed into the water, managed to swim to a nearby ladder, climb to safety and raise the alarm.
The man, who could not swim, was pulled from the water by police and was unable to be saved despite the efforts of paramedics and two other men who jumped in to help.
Police say the pair were pushed from behind by a person who was trying to steal the woman's handbag.
Detective Inspector David Gill said the man and woman were sitting near the edge of wharf talking.
"This is a disgraceful, cowardly act that has resulted in a terrible tragedy," he said.
"A tragedy that will haunt the young (woman) for the rest of her life, along with the family and friends of the (man) and the two members of the public and officers (involved).
"We are calling on the person or people involved to come forward to police to assist us with our investigation so we can help provide closure to the family involved."
The man was pulled onto the deck of a nearby police boat but could not be revived. (Ethan James/AAP PHOTOS)
Det Insp Gill said police were treating the matter as a "very serious" criminal investigation.
"We're in the process of notifying next of kin so we're unable to provide further details about the victim at this stage," he said.
"I would like to recognise the heroic efforts of the passing members of the public who entered the water in an attempt to rescue the man (and the) outstanding efforts of our responding police and emergency service personnel under very difficult circumstances."
There was no evidence alcohol played a role in the man's inability to swim, Det Insp Gill said.
Police divers will search for the handbag, which has yet to be found.
Princes Wharf is a short walk from the Hobart CBD and features restaurants and bars.
Two Victorian men have died in separate incidents at the city's waterfront in recent years after falling into the water.
Dr Robert Bo Xu drowned in November 2019 and Jarrod Robert Davies, who was visiting Tasmania with his father, drowned in February 2020.
A coronial inquest into their deaths, which is yet to deliver findings, has been told both men had consumed a considerable amount of alcohol.
9°C