Police chief Alejandra Giordano told local reporters: "An autopsy is taking place to discover what happened. Apparently he suffered a fall in an area where there are a lot of rocks.”
Mr Minn, a former FZY participant, arrived in Ushuaia, known as “the end of the world”, on Sunday night before leaving the hostel on Monday.
When he had not returned that evening hostel owners alerted the police, and Mr Minn’s body was discovered by a group of trekkers on Wednesday.
His sister, Hayley, 26, a journalist for the Daily Mirror, tweeted on Thursday: “We got the devastating news we didn’t want and it’s breaking my heart."
Mr Minn started what was intended to be a seven-month tour of South America after working at an American Jewish summer camp in New Hampshire, Camp Tevya.