Ordering the inquiry, Antony directed the Army to take strict action against anyone found guilty.
Earlier, the Army had ruled out any inquiry into the matter contending that the youth was a militant as weapons were recovered alongside him.
"For us there is nothing to prove ... It is clear. Army is a disciplined force and carries out operations with honesty and integrity," General Officer Commanding of the Army's 15 Corps Lt General Om Prakash told reporters on the sidelines of a function in Srinagar.
He said the operation in which the youth was killed in Bandipora district on Tuesday night was based on intelligence inputs about movement of militants for the past three days through the area.
"During this operation, movement was observed late in the night. When they were challenged, they opened firing first which was retaliated. One person was killed and weapons were also recovered from the spot," Lt Gen Prakash said.
Hilal Ahmad Dar, a resident of Aloosa in Bandipora district, was killed in army firing late on Tuesday night, triggering protests in the area.
The local residents have alleged that Dar was killed in custody.
