Players from both teams kneeled, some bowing their heads and crossing themselves in prayer.
Chapman was taken to Banner Del E. Webb Medical Center in Sun City. He was then transferred to Banner Good Samaritan Medical Center.
Perez appeared to be in tears as he left the field, and first baseman Eric Hosmer hugged him. Perez quickly left the clubhouse without speaking to reporters. Hosmer hit a line drive off the head of Tampa Bay's Alex Cobb last June. Cobb sustained a concussion.
Playing right field, Reds teammate Jay Bruce heard the ball hit Chapman.
"It was one of the more frightening and non-fun moments I've been a part of on the baseball field," he said.
After Chapman was driven off to the waiting ambulance, Price and Yost met with the umpires.
"It was really a mutual agreement," crew chief Chris Guccione said. "Players were rattled. The staff was rattled. The umpires were rattled. We figured it was best, along with both teams in agreement, that the game should end."
Yost said neither he nor his players wanted to keep playing. Price felt the same way.
"You can't find it in your heart to go out there and play," he said.
Oakland pitcher Brandon McCarthy, who had emergency surgery after he was struck in the head by a line drive in September 2012, urged caution in a post on Twitter.
"all reporting at this point means zilch, until he gets a scan," he said in a tweet.
Chapman, who throws a 100 mph fastball, had walked four Royals in the inning before being injured.
The two-time All-Star had 38 saves for the Reds last season.
When reporters walked into the Royals clubhouse, third baseman Mike Moustakas asked a team official to request that they leave.
"No one wants to talk," Moustakas said.