She would not say if the injuries were life threatening or confirm if the man had lost his leg as had been speculated.
A Falcon Bay Beach Cafe worker told AAP that two men rushed in asking for ice, saying someone's leg had been bitten off.
A spokeswoman for the City of Mandurah said the beach had been closed from Falcon Bay to Westview Parade, including Yeedong Bay.
Surf Life Saving WA tweeted earlier in the day that there was a public report of a 3.5-metre white shark sighted shortly before 8am (WST) at Pyramids Beach in nearby Dawesville, about 1.8km offshore.
The last shark attack in WA was in October, when there were two incidents that resulted in minor injuries.
A grey nurse shark was probably responsible for biting 18-year-old Eli Zawadzki on the foot while he was surfing at Pyramids Beach in Dawesville.
Later that same month, a man was bitten by a shark off WA's southern coast in Albany while diving from a boat and spearfishing, suffering minor injuries.
- AAP