The man, whose name has not been released, was about 650 feet offshore from an isolated beach on Wedge Island with a friend when he was attacked by the shark, The (Melbourne) Age reported.
"The two people were in the water surfing or waiting for a wave when the victim was attacked by a shark," said Tony Cappelluti from the Fisheries Department. "No body has been recovered, but from eyewitness accounts we presume he has been killed."
Cappelluti said the man's friend and two other surfers who were nearby were unable to help the victim and swam to shore.
Officials are searching for the shark, which is believed to be a great white, The West Australian reported.
Fisheries Minister Norman Moore said if the shark is found it will be killed.
The surfer is the fifth person to die from a shark attack in Western Australia since September, officials said.
"It is a shock to everyone that this has happened. The community itself at Wedge is pretty small, but a lot of people come up from Perth to use that area as a holiday playground," said Dandaragan Shire President Shane Love. "My thoughts are with the family and the person's friends."
Notable deaths of 2014 [PHOTOS]