The Defense Ministry had announced that the prince, 29, a Royal Air Force search and rescue pilot, would be posted there for six weeks next year.
The deployment, coming shortly before the 30th anniversary of Argentina's defeat in the Falklands War, seemed to anger some in Argentina.
"Prince William, along with his brother, Prince Harry, is a regular member of the armed forces and they do their stint in the roster that comes all our ways," Britain's chief of armed forces, David Richards, told Sky News.
Britain has ruled the Falklands, 290 miles east of Argentina's coast, for more than 180 years, but Argentina claims sovereignty over the islands, which it calls Las Malvinas.
William, second in line to the throne, begins the deployment in February. His uncle, Prince Andrew, served in the Falklands conflict as a Sea King helicopter pilot.