The woman, named locally as Cindy Waldron, 46, from Lithgow in New South Wales, was reportedly swimming with a friend on Sunday evening at Thornton Beach near Cairns in north Queensland.
She was in waist-deep water when she was attacked, media reports said.
The last fatal attack in the area occurred in 2009, according to the Australian Broadcasting Corporation.
“We hold grave fears for the welfare of the woman,” police spokesman Russell Parker said.
Her 47-year-old friend tried to grab her and drag her to safety unsuccessfully, he said.
“The friend then ran to a nearby business and raised the alarm, and from that point police and other authorities were advised.
“They had been walking along the beach and decided to go for a swim just in waist-deep water at Thornton Beach and probably a very nice, clear night, but obviously may not have been aware of the dangers.”
Nine News reported that witnesses heard the woman yell: “A croc’s got me, a croc’s got me.”
Neil Noble, of the Queensland state ambulance service, said a five metre crocodile had been reported recently in the area.
A search for the missing woman, helped by a rescue helicopter, resumed on Monday. A local cafe is being used as a command post by the search team.
The woman’s friend is being treated for grazes and shock.
Residents told Australian media that the area was a known crocodile habitat.
And local MP Warren Entsch said the area was popular with crocodile-spotting tours and there were many warning signs.
“This is a tragedy but it was avoidable,” he told reporters.
“If you go in swimming at 10 o’clock at night, you’re going to get consumed.”
Crocodiles are common in Australia’s tropical north and kill an average of two people each year. - ABC