Police said Johnson was in the area on a boat, and diving at the moment of the attack.
"A woman who was on board the boat at the time of the incident has been returned to shore, and has been taken by St John Ambulance to hospital," police said.
She was suffering from shock.
The search for Johnson's body is still ongoing as fisheries officers, police air wing and divers conduct patrols in the area.
Glen Quinlivan, one of the first responders, told the West Australian he was setting up his boat for a day trip when he heard cries for help.
"We tried to find him. We tried to help her but to no avail," he said. "I really feel for her, she's obviously witnessed something you don't want to see."
A SharkSmart alert from the Surf Life Saving WA Twitter account warned of a public report of a white shark at Cull Island at 9.39am WA time on Sunday.
Public report white shark sighted 09:39hrs 05/01, Cull Island, Esperance