Miss Finch, 20, was touring a Northern Territory crocodile farm when a 5m saltwater crocodile named Eric took a fancy to her.
When Miss Finch was allowed inside Eric's enclosure to watch him being fed, the reptile, who was supposed to be enjoying a lunch of raw chicken at the time, lunged at her.
Startled by the sudden move, she jumped out of the way and ran to safety.
Later, the former model laughed off the encounter.
"As soon as I saw him move I got nervous," she said.
Miss Finch, who hails from Queensland, told the Northern Territory News that the incident was one of the more unusual events she has been involved in since being announced the Australian winner of the Miss Universe contest in April.
Charlie Manolis, Crocodylus Park spokesman, said Eric the crocodile had been removed from a river three years ago after he began "looking at fishermen the wrong way".
"He's a nice old croc, but I wouldn't like to be on the wrong end of him," Mr Manolis told The Brisbane Times.
"There's always an element of, you know, something not going to plan."
However, he said Miss Finch had not been in danger.
"We don't normally do that (allow non-trained people inside the enclosures)...but on special occasions we can go in and feed him with other people present with special security measures in place.
"He's pretty predictable. I don't think we would have seen the headline 'Croc Eats Miss Universe' in the papers this morning."
Miss Finch will now travel to the Bahamas to represent Australia in the international finale of Miss Universe next month.