28-year-old Li Hongyang, a security trooper from the 62nd Combat Service Support Battalion, fainted after completing his 2.4km run at 8:38am.
He was undergoing his IPPT at Kranji Camp III on Tuesday, said a statement released by the ministry on Tuesday afternoon.
After being attended to by a medic on-site, he was brought to the Kranji Medical Centre where a Singapore Armed Forces (SAF) doctor attended to him five minutes later.
Li was then sent in an ambulance to Khoo Teck Puat Hospital at 9am. Despite continued attempts to resuscitate him en route to the hospital, Li was pronounced dead at 9:40am, 20 minutes after reaching there.
The ministry said it is assisting Li's family, which has been notified of his death, and is currently investigating the incident.
"Hongyang was a cherished member of the battalion," said Li's commanding officer, Lieutenant-Colonel (NS) Gan Fong Yin. "We will miss him and our hearts go out to his family."