Dozier, who left with a quad contusion and neck discomfort, was placed on the seven-day concussion injured list, and the club recalled Kelvin Gutierrez from Triple-A Omaha prior to Game 2 of the doubleheader.
Abreu is day-to-day after leaving the game with a facial contusion, laceration and bruised left knee. The initial assessment for a concussion was negative.
"He's doing well enough that he wants to play the second game [of the doubleheader]," White Sox manager Tony La Russa said. "He's bruised. He's sore. It could have been worse. ... There's a sense of relief."
The nasty collision occurred after Dozier popped up right in front of home plate. As Sox catcher Yasmani Grandal and Abreu converged on it, Dozier started to run to first base, and, while avoiding Grandal, he ran right into Abreu, who was looking up at the ball.
The two hit the ground hard. They lay next to each other for several moments as they were attended to by their respective training staffs. Eventually, both walked off the field with assistance.
"It was extremely scary in the moment," White Sox pitcher Lucas Giolito said. "That was a big collision. [Abreu's] taking some hits and gets right back up. After a minute, he got up and said he was fine and could keep playing. That's the type of player that he is. He'll do anything for this team.
"It was a huge relief going in and seeing he's good, in high spirits. He'll probably be back playing tomorrow."
Abreu is the reigning AL MVP and a big part of Chicago's success this season. Dozier has been struggling and is in the midst of an 0-for-31 skid. Grandal took over at first base, and Zack Collins came in to catch for the White Sox. Hanser Alberto took over at third base for the Royals, who ended up snapping an 11-game skid with the 6-2 win.