Police in Shizuoka, one of two prefectures that include Japan's highest mountain, began the search Tuesday after receiving calls from some viewers of the livestream.
Police found the body at an altitude of about 3,000 meters (9,800 feet) and are checking whether it is that of the man in the video, a police official said on customary condition of anonymity.
The video, titled "Let's Go to Snowy Mt. Fuji," shows a man who identifies himself as TEDZU panting. "I'm rushing to the peak," he says.
The man complains repeatedly about his cold fingers. "My fingers are killing me. But I have to operate my smartphone. I should have brought a hot pack," he says.
He then tries various ways to warm his hands, including sticking one under his arm. The snow-covered path becomes narrower as he walks along a cliffside fence. Then the path slopes down and the man cautions himself against falling.
"Oh, this place is slippery, getting dangerous," the man says. "I'm trying to walk by the rocks, yes, rocks. It's a steep downhill."
"Wait!" he says. "I'm slipping." The noise of his slide can be heard on the video.
The fall accelerates. The video shows him sliding feet-up, with his hiking sticks hurtling away, before it ends abruptly.
Mount Fuji's climbing season ended last month. There is no law prohibiting climbers from entering the mountain at other times, police say.