Doug was found with pellet wounds to his ribs and abdomen at the base of a tree at a Morayfield property, north of Brisbane, on Tuesday morning.
His mother Meryl was also shot but is expected to make a full recovery after earlier surgery.
Staff at the Australian Wildlife Hospital tried to remove half of one of Doug's lungs after a pellet was found in his chest.
"However, it is with sad regret that during surgery, Doug passed away and vets were unable to save him," a spokeswoman said.
X-rays on Friday revealed surgery was needed as soon as possible after it was found his condition had worsened.
He was given only a 50-50 chance of survival before the operation.
Authorities are continuing to search for the person who shot the mother-and-baby koalas.
