The 29-year-old French national yelled "Allahu Akbar" before stabbing the woman, police said.
A British woman was stabbed to death on Wednesday at a backpackers' hostel in Australia and two people were injured, one seriously, in what police say may have been an "extremist" attack.
A spokesman for Queensland state police said the suspected attacker, in Australia on a tourist visa, was a 29-year-old French national who had yelled "Allahu Akbar" (God is greatest) when arrested.
A 21-year-old British woman died at the scene of the attack, south of Townsville in the state's far north, police said. A 30-year-old British man was in critical condition in hospital.
"Initial inquiries indicate that comments which may be construed of being of an extremist nature were made by the alleged offender," Queensland Police Service Deputy Commissioner Steve Gollschewski told reporters.
"This person appears to have acted alone," he said. "He is a visitor to Australia and has no known local connections, however investigations are ongoing."
About 100 people have left Australia for Syria to fight alongside organisations such as Islamic State, Australia's Immigration Minister said earlier this year.
Australia, a staunch U.S. ally, has been on heightened alert for attacks by home-grown radicals since 2014 and authorities say they have thwarted a number of plots.
There have been several "lone wolf" assaults, including a 2014 cafe siege in Sydney that left two hostages and the gunman dead. Also in 2014, police shot dead a Melbourne teenager after he stabbed two counter-terrorism officers.
In 2015, a 15-year-old boy fired on an accountant at a police headquarters in a Sydney suburb and was killed in a gunfight with police.
Police did not give details of the other person wounded in the attack, which was captured on video and witnessed by more than a dozen people. There was no ongoing threat to the community, Gollschewski said.
A dog was also killed in the attack, he added.
© Thomson Reuters 2016
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