Sexton and Ryan, two of Farrell's most important players, were replaced due to suspected concussions during last week's opening 21-16 loss to Wales.
Ireland played most of the game with 14 men following Peter O'Mahony's 14th minute red card.
Billy Burns will win just his fifth cap in place of Sexton, while Ulster's Iain Henderson will fill the big hole left by Ryan and will captain the side for the first time.
Former Blues and Hurricanes halfback Jamison Gibson-Park will start at nine in place of Murray, who injured his hamstring in training.