The move was made before Tuesday's game at Minnesota, where Salazar was scheduled to start after being recalled from Columbus.
Salazar was in the rotation from opening day until he was sent to Columbus May 16, making eight starts for the Indians while going 1-4 with a 5.53 ERA. He made 10 starts for Columbus and posted a 2.32 ERA with 39 strikeouts in 31 innings over his last five turns.
The Taiwan-born Lee made 15 appearances over two stints with the Indians this year, compiling a 4.26 ERA. He pitched in the last two games, totaling four outs and allowing five runners with two strikeouts.