"The missing surfer is believed to be an adult male."
Premier Mark McGowan said the man was in the water with other surfers at the time of the attack.
"One of the surfers tried to get him from the water but was unable to do so," he told reporters.
"I'm advised either his whole surfboard or part of his surfboard has been recovered."
"A witness called to say they saw a shark attack a person," ambulance service spokeswoman Joanne Hill said. "We went to the scene. I understand they still haven't found anybody."
Surf Life Saving WA tweeted there was a public report of an unknown species of shark sighted just before 9.30am.
The attack was reported just over an hour later.
Shire of Esperance president Ian Mickel told the NCA NewsWire the community was saddened by the tragedy.
"It's extremely sad to hear there's been a shark attack again," he said.
"We've had a lot of attacks over the last seven years.
"It's just really, really disappointing."
Esperance Ocean Safety and Support committee member David Swan told the NCA NewsWire everyone was devastated.
"Our thoughts are with the family and close friends," he said.
"Everyone's in a bit of shock and feeling very sad."
Swan said he hoped McGowan would soon be willing to meet with the committee about mitigating shark attacks in the area.
"I invite and strongly hope the Premier will come down and see us, and listen to our concerns and our solutions," he said.
"He showed great leadership through COVID-19 and I would like to see some leadership on this too."
Beaches have been closed from Wylie Head to Cape Le Grand National Park.
Kelp Beds is a popular surf break and is where Laeticia Brouwer, 17, was fatally bitten on the leg while surfing with her dad in April 2017.
Surfer Sean Pollard was also mauled at Wylie Bay in 2014, losing his right hand and left arm, but he survived the attack.
In January, experienced diver Gary Johnson was taken by a shark near Cull Island, close to West Beach in Esperance.
