Major League Baseball announced the move before Game 2 between the Braves and Houston Astros on Wednesday night.
Morton suffered a broken right fibula after he was struck on the lower right leg by Yuli Gurriel's 102-mph comebacker in the second inning of Atlanta's 6-2 win in Game 1 on Tuesday. Morton initially stayed in the game, but exited in the third inning.
Morton will be sidelined until spring training.
The 25-year-old Davidson had a 3.60 ERA in four big league starts this season, all in May and June, after making his debut in the majors in 2020. He was 2-2 with a 1.17 ERA in four starts at Triple-A Gwinnett, making his last appearance on Oct. 3. He missed much of the season with left forearm inflammation.
Davidson has not appeared in any major league postseason games.