Royals pitcher Yordano Ventura received a seven-game suspension, while teammates Edinson Volquez (five games), Lorenzo Cain (two games) and Kelvin Herrera (two games) also were disciplined. All four also received undisclosed fines.
Royals manager Ned Yost indicated all four players would appeal.
"We understand that Major League Baseball has to do what they think is fair in situations like this," Yost said in a release. "Now, we just have to wait for the appeals process to play out."
Royals general manager Dayton Moore said the suspensions were expected.
"There are going to be consequences for your actions," Moore said by phone. "Any time you have this type of activity, the end results are going to be suspensions or injury."
Moore said he does not fault his team's behavior this season.
"We have a team that plays with a lot of passion and a lot of energy," he said.
Herrera already is appealing a five-game suspension he received for throwing behind Oakland's Brett Lawrie last weekend at Kauffman Stadium.
Ventura was fined during the Oakland series for hitting Lawrie with a pitch -- Lawrie triggered harsh feelings between the clubs when he slid hard into Royals shortstop Alcides Escobar in the series opener, injuring Escobar's knee.
Ventura, though, seemed remorseful and apologetic earlier this week, and vowed he would better control his emotions.
But on Thursday, Ventura stared down Chicago's Adam Eaton after Eaton hit a comebacker to the mound. Eaton shouted something initially at Ventura, who then shouted back at Eaton before both benches emptied.
In the ensuing melee, White Sox right-hander Jeff Samardzija was seen trying to go after Cain, who was hit by a pitch from Samardzija on Opening Day. Volquez was seen trying to punch Samardzija, though he missed badly.
Cain said afterward he would be surprised if he got disciplined because Samardzija came after him. Samardzija received a five-game suspension.
White Sox left-hander Chris Sale, who also received a five-game suspension, reportedly tried to get into the Royals' clubhouse after the incident while the game was still in progress, apparently looking for Ventura. Sale neither confirmed nor denied the report to Chicago reporters.
All suspended players will remain available until the appeals process is played out.
But if the appeals don't shorten or wipe out any of the Royals' suspensions, the Royals at some point could have to play with a 21-man roster.
"As I said, there are consequences for actions like this," Moore said. "It's just something we'll have to deal with as an organization."