The Black Hawk, part of the Air Force Rescue Team, took off at 7.54 a.m. from Songshan air force base, 4.9 km from Taipei, and was en route to a military base in northeastern Yilan county's Dong'ao, reports Efe news.
It disappeared from the radar at 8.07 a.m. and made a forced landing in the mountains of New Taipei City's Wulai district.
The activity was reportedly part of a New Year's inspection and the cause of the accident is not yet known.
Addressing the media here, Air Force Commander-in-Chief Hsiung Hou-chi said that the last communication with the crew took place at 8.06 a.m. and the chopper disappeared from radar screens a minute after that, reports Taiwan News.
Besides Shen, the other victims were also high-ranking military officials, the Defence Minister said, adding that five other passengers were alive and receiving treatment.
In addition to three crew members, nine military officers were on board, as well as a reporter from the Military News Agency.
Shen, 62, was Air Force commander general and vice minister of defence before he took up his post as chief of general staff in July 2019.
The pilot, Col Yeh Chien-yi, who died in the crash, had 261 hours of flight experience in the UH-60M and another 2,214 in its civil version, the S-70C, the local United Daily News reported.
The helicopter, in service from July 2018, had accumulated 376 flight hours and had not presented any major problems in the last three months, UDN added.
The Black Hawk helicopter is thought to be one of 60 UH-60Ms purchased from the US in 2010.
"My deepest condolences go out to the outstanding servicemen lost in today's helicopter crash, as well as their families. We will do everything we can to help their families in this time of loss & investigate the cause of the crash," President Tsai Ing-wen said on Twitter.
The accident comes nine days ahead of Taiwan's 2020 presidential election on January 1.
Tsai announced after the accident that she will suspend her election campaigning activities for three days for mourning.
( With inputs from IANS )