Andrew Paice was on an hour-long wildlife cruise on the Adelaide River with his partner and seven-year-old daughter on Tuesday when they spotted something unusual on the riverbank.
Earlier they had watched as crocodiles, including the huge 5.5-metre (18-feet) male known as Brutus, leapt out of the water to eat a piece of buffalo meat held out on a pole to them.
"It was on the way back to the jetty, we went past Brutus again, he was up on the bank," Paice told AFP from Kakadu National Park in the Northern Territory on Wednesday.
"As we were going past, we noticed that there was a fin. We thought it was a barramundi (fish) or something.
"And the guide took the boat in for a closer look and lo' and behold... it was a shark."
Brutus, who is thought to be about 80 years old and is missing a front leg and most of his teeth, is well known in the area, and the Northern Territory News described the battle as "Jaws v Claws".
Speculation is that the prospect of a fish dinner was tasty revenge for a croc that was thought to have lost his limb to one of the sharks who inhabit nearby waters.
"But from listening to other people, it was probably more likely a big crocodile (which took his front leg). But who knows? It was either a crocodile or a shark," Paice said.
His daughter was "awestruck" by the experience.
"So were the rest of the people including the guide; he had never seen it before either and he had been there for about 30 years. He was so excited."
The Northern Territory News said Brutus won the titanic struggle with the shark, but Paice said he wasn't so sure.
"When we went past the first time the croc was lying there with the shark in its mouth," he said.
"When we pulled the boat in closer it slid back into the water. And when the shark, or the mouth of the croc, hit the water, the shark started to thrash around.
"So it was certainly still alive. We couldn't see any blood anywhere," he said, noting that Brutus had only a few teeth left.
"It may have got away; it may have got eaten -- we don't know. He didn't put that display on for us unfortunately."