Chapman was carted off the field and transported by ambulance to a hospital and would be kept overnight for observation, the Reds said on their Twitter account.
The Reds said Chapman was originally taken to Banner Del E. Webb Medical Center in Sun City, Ariz., where tests indicated the facial fractures. He was then transferred to Banner Good Samaritan Medical Center, where he was to undergo further testing.
Reds manager Bryan Price said Chapman was conscious and talking as he was taken off the field during the game against the Kansas City Royals.
"Not good," Price said. "He left the field on a stretcher, took a line drive just above his left eye is what it looks like -- a contusion, a laceration -- and certainly needs to be taken to the hospital and checked. We've got Tomas Vera, an assistant trainer, is going to be with him. And then we'll get our updates from there."
The hard-throwing left-hander was struck by Salvador Perez's drive with two outs in the sixth inning. He crumbled to the ground, face down and flailing his legs. The ball caromed into the third-base dugout. Medical personnel, including Royals team doctor Vincent Key, rushed to the pitcher. Chapman's father was among the people to run onto the field.
Players from both teams huddled around the mound as the 26-year-old Cuban was being attended to and the stadium fell silent. An ambulance's siren could be heard in the background while Chapman was lifted onto the stretcher.
"I know this isn't uncommon as we would like it to be, but it was frightening, certainly frightening," Price said.
The game was then called with Kansas City leading 6-3.
Chapman, who throws a 100 mph fastball, had walked four batters in the inning before being hit.
The two-time All-Star had 38 saves for the Reds last season.
In January, baseball approved protective caps for pitchers after several terrifying incidents similar to this one in the past few years.
The heavier and bigger hats were available for testing during spring training on a voluntary basis, but the cap apparently would not have helped Chapman in this case.
Arizona pitcher Brandon McCarthy, who had emergency surgery after he was struck in the head by a line drive in September 2012 when he was with Oakland, urged caution in a Twitter post.
Reds third baseman Todd Frazier also weighed in with a tweet.