Senior Sergeant Justin Tarasinski said up to eight surfers were in the water at the time of the attack.
"The surfboard washed up nearby to where the attack occurred and with obvious signs of shark attack," he told reporters.
"The chances of survival are obviously pretty slim considering some of the accounts that have been provided to us."
The search, involving jet skis and boats, was to end at sunset and would resume this morning, with the addition of police divers.
Premier Mark McGowan described it as a "very sad and potentially tragic" situation.
"One of the surfers tried to get him from the water but was unable to do so," he told reporters.
Jess Gardiner said she was swimming less than 1km away with her young daughter around the time of the attack.
"My partner had seen what he thought was to be a shark behind me, about 50 to 100m away from me," she told 9 News.
"He said it was anywhere between a 2 to 3m shark ... panic set in.
"There was a fair few families and kids throughout the bay."
Shire of Esperance president Ian Mickel said 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 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."
McGowan said his government was doing what it could to mitigate the risk of shark attacks in WA, including more affordable Shark Shields and helicopter patrols.
He also said the water off Esperance was a "breeding area" for white sharks.
"There's always a risk when you go in the water," he said.
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.