The school said both players were sent home from Hawaii and would miss Saturday's game versus Hawaii and Wednesday's game versus Saint Mary's in Las Vegas.
"I'm very sorry for this incident," Sidney said in a statement released by the university. "I had no intention of this ever happening. I apologize for embarrassing my family, all the Mississippi State fans, my teammates and coaches.
"I will learn from this and move on."
Bailey, a captain and Sidney's roommate on the trip, was equally apologetic.
"I want to apologize to Mississippi State, to the people in Hawaii and to the fans that were in the stands that witnessed everything," Bailey said in a statement. "Due to me being a captain, I should have handled the situation in a much different way. It should have never gotten to the point that it did. I really am sorry that all of this happened, especially with it unfolding on TV like it did."
The length of their suspensions will be determined by the players' actions going forward. The coaching staff will reassess the situation when the Bulldogs return to campus.
"Our athletic staff, coaches and student-athletes have a responsibility to conduct themselves in a manner that brings credit and honor to our university," athletic director Scott Stricklin said in a statement. "The actions that took place Thursday night in Hawaii were embarrassing to all of us who love Mississippi State University and our athletic program. This behavior will not be tolerated."
Punches were thrown in the fight, which lasted several minutes and was broken up by teammates.
"In my 13 years as a head coach, we've never had anything like this happen before," coach Rick Stansbury said in a statement. "I am very disappointed in the actions of Elgin Bailey and Renardo Sidney and in no way does it reflect the overall picture of our program. It is not how we want our men's basketball team to be viewed nationally, and it is certainly not the conduct we expect of teammates in our program, nor will it be tolerated on any level."
Sidney scored 19 points in the Bulldogs' 69-52 win over San Diego earlier Thursday while Bailey had two points.
Sidney, a highly touted McDonald's All-American out of Fairfax (Los Angeles) High, sat out all of last season while awaiting clearance from the NCAA. He has appeared in just two games this season and scored 31 points with nine rebounds. Just this week, he was suspended by Stansbury for "conduct detrimental to the team" and was benched for the first-round loss to Washington State on Wednesday.
Bailey has started 10 of the 11 games this season, and is averaging 6.2 points and 3.9 rebounds.
Information from The Associated Press was used in this report.