The 31-year-old jawan was suffering from lung cancer. He was being treated at the military-run Base Hospital here.
His sample was taken for COVID-19 test and the results came as positive, they said.
The jawan, a native of Maharashtra, was posted at Itarana Cantt in Alwar district of Rajasthan, police said.
The police said they received information about the incident at around 4 am at Naraina Police Station.
On visiting the spot, the jawan was found hanging with a nylon rope from a tree behind the COVID-19 ward of the hospital, Deepak Purohit, Deputy Commissioner of Police (West) said.
No suicide note was found at the spot, he said.
He was suffering from lung cancer and was under treatment at the Base Hospital since May 5. He also tested positive for coronavirus, the official said.
The jawan was last seen at around 1 am on Tuesday when he went to the washroom situated behind the COVID-19 ward, he added.
The body has been shifted to the mortuary of the hospital, police said.
Family members of the deceased living in Alwar have been informed about the incident, they said, adding postmortem will be conducted in the presence of his family.
AMP SRY