A Haley aide told The Associated Press the Republican governor will have outpatient surgery Friday for "radial nerve compression," or carpal tunnel syndrome.
Haley is transferring authority under a constitutional provision that says the lieutenant governor shall have full authority to act in an emergency in the case of the governor's temporary disability or absence.
Spokesman Rob Godfrey says McGill could be the acting governor for several hours, starting at 7 a.m.
Godfrey says doctors attribute Haley's injury at least partly to her hand-signing 39,000 letters since taking office.
McGill became lieutenant governor last month. No Democrat has been in the state's top spot since January 2003.