Health authorities are warning people not to eat wild shellfish from the east coast of Tasmania due to the risk of potentially fatal paralytic poisoning.

Blooms of toxin-producing algae off the east coast, including in waters around Hobart, means there are high levels of toxins in the state's shellfish.

"Shellfish feed on algae and concentrate the toxin - this makes them dangerous to eat and may cause serious and even fatal illness," the state's acting director of public health, Dr Mark Veitch, said in a statement on Sunday.