Chief of Defence Staff Gen Bipin Rawat, his wife and 11 others died after the Mi-17V5 helicopter came down in hills near Coonoor city on Wednesday morning.
One survivor is being treated for his injuries in hospital.
Gen Rawat, 63, was appointed India's first-ever Chief of Defence Staff in January 2019.
This brought together the Army, the Navy and the Air Force, and Gen Rawat had been in charge of a range of operations including in Indian-administered Kashmir.
The Indian Air Force said it had ordered an investigation into the accident, which happened in foggy weather. A cabinet security committee is holding an emergency session, chaired by Prime Minister Narendra Modi.
On Twitter, Mr Modi said: "[Gen Rawat] brought with him a rich experience of serving in the Army. India will never forget his exceptional service.
"A true patriot, he greatly contributed to modernising our armed forces and security apparatus. His insights and perspectives on strategic matters were exceptions. His passing away has saddened me deeply."