The small adult whale remains stranded after an attempt by volunteers to refloat it on Monday failed amid rough weather.
“The fact that the whale re-stranded itself may be an indicator that the whale is not healthy, and its stranding was not accidental,” DELWP wildlife emergencies officer Mandy Watson said in a statement.
The whale will be stabilised in shallow water so a vet can examine it while a new course of action is determined, DELWP says.
The department has advised people not to approach within 300 metres of the stranded whale without authorisation.
If the whale is indeed a dwarf sperm whale, it will be the second time in as many days a member of the rare species has become stranded on a Victorian beach.
Melbourne Museum is currently analysing the skeleton of a 2.42m female whale that died after becoming stranded at Lake Tyers Beach, in Gippsland, on April 30, to determine if it’s a dwarf sperm whale.
There are early indications she belonged to the rarely seen dwarf sperm whale species, the Kogia sima, which is also the smallest whale species in the world.