The 25-year-old American was batting in the bottom of the first inning against the Los Angeles Dodgers in suburban Phoenix when he was hit on the right side of his mouth with a pitch thrown by 23-year-old Mexican left-hander Julio Urias.
Calhoun fell to the ground instantly on his back and stayed down for about 10 minutes as Rangers trainer Matt Lucero treated him before he was driven off the field in an equipment cart.
Calhoun, who did not lose consciousness, suffered bleeding inside of his mouth. He was taken to St. Joseph's Hospital in Phoenix for further examination and treatment.
Dr. Jeffrey Edelstein was set to examine him. The specialist treated former Rangers minor league coach Howard Johnson when he was hit in the face by a foul ball near the end of pre-season training in 2018.
Rangers manager Chris Woodward drove to the hospital to be with Calhoun, leaving bench coach Don Wakamatsu to guide Texas for the remainder of the game.
Calhoun was taken by the Dodgers in the fourth round of the 2015 MLB Draft and was among the players traded to Texas in 2017 in a deal that brought Japanese pitcher Yu Darvish to the Dodgers.
Calhourn batted .269 with 21 home runs and 48 runs batted in over 83 games for the Rangers last season after hitting two homers and driving in 11 runs over 35 games for Texas in 2018, when he went .222 at the plate.