The Nationals announced the switch Sunday morning, less than nine hours before the game is scheduled to begin.
Scherzer had been expected to take the mound Sunday for Washington in the tied series. But that plan was thrown into question after he came on in relief in Game 2 and struck out all three batters he faced in a 4-2 victory at Los Angeles on Friday night.
Scherzer will instead start Game 4 on Monday, manager Dave Martinez announced later Sunday.
Sanchez went 11-8 with a 3.85 ERA this season, his first with the Nationals. He is 2-5 with a 3.12 ERA in eight previous postseason appearances for Detroit and Atlanta. He started one game of last year's NLDS between the Braves and Dodgers, allowing three runs in 4 2/3 innings and taking the loss for Atlanta.
He was 0-1 with a 3.18 ERA in two starts against the Dodgers this season.
Washington also announced that center fielder Victor Robles, who left Game 2 early, had an MRI and was diagnosed with a mild hamstring strain. Michael Taylor will start in his place, but Martinez said Robles will be available to pinch-hit in an emergency.
The Associated Press contributed to this report.