The 32-year-old felt a slight strain in his hamstring on Wednesday and will not be risked.
Larkham admitted pushing himself during training and said he had possibly overdone it with too much kicking practice.
He is expected to be fit for the second Test in Brisbane on June 2.
Waratahs fly-half Sam Norton-Knight has been promoted from outside the 22-man squad directly into the starting XV.
Norton-Knight said he felt sorry for Larkham but was "shocked and excited" to be handed his first Australia cap.