Rodriguez, who was traded from the Houston Astros on Tuesday, will pitch against his former team on Saturday.
Erik Bedard, who was scheduled to start Saturday, will be pushed back to Monday.
Pittsburgh manager Clint Hurdle says taking Correia out of the rotation was a difficult decision, especially since he is on a six-game winning streak. But he says that it is the best move for the team.
Correia, who is 8-6 with a 4.24 ERA, is unhappy with the move, but says he'll "have to live with it."