Three people had been involved in the base jump at Stockhorn - a mountain of the Bernese Alps.
The operation started around 4pm. Hewetson found himself in difficulty during the descent, then fell on rough terrain.
Two people accompanying Hewetson alerted a Rega helicopter, which rushed to the area to search for him.
Friends and family have taken to social media to pay tribute to the Kiwi.
"Gwill was an inspiration to me," said one friend.
"It's so rare to find your passion in life and have the courage to live it. Whether it was an expedition to the Mariana Trench or jumping off the Eiger, Gwill lived life to the fullest. RIP my friend."
A Ministry of Foreign Affairs and Trade spokesman said they were providing consular assistance to Hewetson's family.
An investigation was under way to clarify the circumstances around the death.
At least three other Kiwis have died in similar accidents in Switzerland.
In 2014, Dan Vicary, 33, died after crashing into a field following a jump from a helicopter over Switzerland's Luetschental Valley.
Two years earlier Te Awamutu man Alan McCandlish, 31, died after hitting a ledge while base jumping, in the mountain region of Berner Oberland.
In 2004, Kiwi Duane Edwin Thomas also died in a base jumping accident in Lauterbrunnen, Switzerland.