The man, whose name has not been released, was celebrating a friend's 30th birthday on Saturday at the Mary River Wilderness Retreat, an Outback tourist destination 70 miles southeast of Darwin, the victim's hometown, Senior Sergeant Geoff Bahnert said.
The victim and another man had swam across the river. The pair were swimming back when the crocodile attacked, he said.
"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," Mr Bahnert said.
Alcohol may have played a part in the decision to swim, he said.
Police and a government crocodile management team are at the resort.
"The advice to tourists is to come, look, take photographs and stay out of the water," Mr Bahnert added.