Jeff Varner, who is appearing on Survivor: Game Changers, made the revelation about his team-mate Zeke Smith on Wednesday's episode.
Varner told the show's presenter and his team-mates: "There is deception here," before turning to Smith and asking: "Why haven't you told anyone that you're transgender?"
He has since apologised on Twitter.
Several other contestants quickly defended Smith after Varner's comments, telling the former news anchor his actions were "so wrong" and that he "didn't have to do that".
Smith had previously shared his history with Varner privately but had not intended to reveal he was trans on the show.
In an article for The Hollywood Reporter published after the episode aired, Smith criticised Varner and said he was "not wild about [viewers] knowing that I'm trans".
He wrote: "In calling me deceptive, Varner invoked one of the most odious stereotypes of transgender people, a stereotype that is often used as an excuse for violence and even murder.
"Varner is saying that I'm not really a man and that simply living as my authentic self is a nefarious trick.
"In reality, by being Zeke the dude, I am being my most honest self - as is every other transgender person going about their daily lives."
Smith added that he doesn't believe Varner, who is gay, did it because he hates trans people, and praised his Survivor team-mates for the way they reacted.
"I think he hoped others would believe that trans people are fraudulent. What's great is that nobody bought it.
"It's important people see he lost that fight. The message should be clear that hate will always lose."
In a Twitter message posted after the show aired, Varner offered his "deepest most heart-felt apologies to Zeke Smith".
He wrote: "I was wrong and make no excuses for it. I own responsibility in what is the worst decision of my life."
Follow us on Facebook, on Twitter @BBCNewsEnts, or on Instagram at bbcnewsents. If you have a story suggestion email entertainment.news@bbc.co.uk.

A skeleton of a meat-eating Jurassic dinosaur, the theropod, was uncovered by spring storms at Lavernock beach, Vale of Glamorgan, in 2014.
The dinosaur's missing foot was found at the beach by palaeontology student, Sam Davies, of Bridgend, at the beginning of this month.
"My first reaction was that I was very lucky," he said.
The fossilised skeleton of the theropod - a distant cousin of the giant Tyrannosaurus rex - went on display at the National Museum Cardiff's main hall in June after it was found by fossil-hunting brothers Nick and Rob Hanigan.
Mr Davies, who studies at the University of Portsmouth, visited Lavernock, near Penarth, after his tutor told him its cliffs were rich with fossils.
He arrived only hours after a cliff fall had exposed the fossil and before it could be washed away by the tide.
"It was pure luck that I found it. It was just sitting on top of a slab of rock," he said.
His tutor, Dr David Martill, confirmed the find was the missing foot of the recently discovered dinosaur, after the student emailed a picture.
Dr Martill said: "This was a chance-in-a-million find and highlights how important it is to encourage fossil hunting in this country."
He said the specimen would help chart the evolution of dinosaur feet.
The foot has been donated to the Amgueddfa Cymru, which hopes to put it on display with the rest of the skeleton soon.
Dr Caroline Buttler, head of palaeontology at the museum, said: "The dinosaur found by Nick and Rob Hanigan is the first skeleton of a theropod found in Wales.
"Sam's find adds to its significance because we can learn more about the animal and how it is related to the dinosaurs that eventually evolved into birds."
A contestant on a US TV show has been outed as being transgender by one of his fellow competitors.
[NEXT_CONCEPT]
The fossilised foot of a dinosaur has been discovered on a south Wales beach, National Museum Wales has announced.