The pair were in shallow water at Thornton Beach in the World Heritage-listed Daintree National Park in Queensland state when the 46-year-old woman was taken by the crocodile late on Sunday, police senior constable Russell Parker said.

"Her 47-year-old friend tried to grab her and drag her to safety but she just wasn't able to do that," Parker told the Australian Broadcasting Corp.

Aljazeera reports conflicting statements as the police said the women were swimming in waist-deep water, while paramedics reported they were wading in knee-deep water when the crocodile struck.

A rescue helicopter fitted with thermal imaging equipment failed to find any trace of the missing woman on Sunday night, Parker said, with the search resuming on Monday with a helicopter, boat and land-based search teams.

Australian federal MP in Queensland Warren Enstch said the beach was beside a creek where tourism operators run crocodile-spotting tours.

Enstch said there are plentiful crocodile warning signs in the region.

"You can't legislate against human stupidity," Entsch said. "If you go in swimming at 10 o'clock at night, you're going to get consumed."