The probe into the alleged incident on 7 August was ordered by Brigadier Bill Wright, commander of the Berkshire military college.
According to a report in The Sun, it is alleged a cadet was pinned down before water was poured over a cloth covering his face.
Prince William and Prince Harry both attended Sandhurst, where all officers in the British Army are trained.
Brig Wright said: “I am aware of allegations about an incident at the Royal Military Academy Sandhurst on August 7 involving some of our officer cadets.
“I have ordered an investigation by the Royal Military Police.
“The Army and I expect the highest standards of behaviour at Sandhurst; anyone found to have fallen short is dealt with robustly, including dismissal, if appropriate.”
The CIA used the interrogation technique in the wake of the September 11 attacks on the US.
The Sun said the three cadets involved are currently on leave and have been moved into separate platoons while the investigation takes place.
Sandhurst’s stated aim is “the national centre of excellence for leadership”. The academy was founded in 1947.