Police say he ignored signs to stay out of the water at a popular camping ground at Mary River, 65 miles (100km) from Darwin, the state’s capital.
The river has one of the highest crocodile populations in the area.
Onlookers watched in horror as the victim was suddenly attacked.
He was last seen in the crocodile’s powerful jaws, reports the BBC’s Phil Mercer in Sydney. Police are searching for him.
The victim and another man had gone swimming across the river, and were swimming back when the crocodile attacked, police say.
“Several of the group in the party witnessed the male being taken in the jaws of the croc for a period of time, and then he was out of sight,” Senior Sergeant Geoff Bahnert is quoted as saying by the AP news agency.
“The Mary River is known worldwide to have the greatest saturation of adult saltwater crocodiles in the world. You don’t swim in the Mary River,” he added.
Saltwater crocodiles can grow up seven metres (23ft) long and weigh more than a tonne; they are a common feature of Australia’s tropical north.