Priestland has failed to shake off a shoulder injury that he suffered during the 22-10 win over Ireland in the last match.
Wales coach Warren Gatland announced that Hook will come in as fly-half against France in the only change to the side that beat Ireland in the quarter-finals.
"Time was against Rhys, but we are happy that we have the talent and ability elsewhere in the squad to cover him," said Gatland.
"Rhys has done everything we have asked of him and more during this World Cup, but, when we have players of the calibre and experience of James Hook and Stephen Jones coming into the squad and starting lineup, there is no sense that Rhys's absence leaves us any weaker."
Hook, 26, has only played three minutes of rugby at fly-half during the World Cup.
Wales meet France at Eden Park on Saturday morning for a place in the World Cup final.