Wiggins is competing in the Tour of California in May while Froome is being rested ahead of the defense of his Tour de France title in July.
The British team will also be without Australian rider Richie Porte, whose season has been disrupted by illness. Porte is looking to be at full fitness to support Froome at the Tour de France.
Irish rider Philip Deignan will compete in his first Grand Tour for the Team Sky. Three stages of the Giro are in Northern Ireland and Ireland.