A diver has been taken to hospital after being bitten by a shark at the Melbourne Aquarium.

The aquarium has confirmed the woman in her 30s was bitten by a 40-centimetre tawny nurse shark during a routine feeding session.

Paramedics say she has been taken to hospital in a stable condition with three cuts to her face.

Aquarium general manager Mark Manteit says the bite is not serious.

"The diver was bitten by one of our smaller 40cm tawny nurse sharks in the Shipwreck Cove exhibition," he said in a statement.

"The tawny nurse shark does not have sharp teeth, they have small plates on the top and bottom of their mouth which they use to feed on small prey."

He says the woman was taken to hospital as part of the aquarium's standard operating procedures.

"While we ensure that we adhere to the best practice operating procedures for the care and management of animals at the aquarium, the nature of our business is such that these incidents will happen from time to time," he said.