In the midst of a heated playoff race, the Cleveland Indians have traded right-hander Trevor Bauer to the Cincinnati Reds and received outfielders Yasiel Puig and Franmil Reyes as part of a three-team deal that includes the San Diego Padres.

As part of the trade, the Indians also received left-hander Logan Allen and minor league infielder Victor Nova from the Padres and minor league pitcher Scott Moss from the Reds. Cincinnati outfield prospect Taylor Trammell, ranked No. 14 on Keith Law's midseason top prospects list, was sent to San Diego.

Cleveland (62-44) is three games behind the Minnesota Twins in the American League Central and has a 2 ½-game cushion atop the wild-card standings.

Following Cleveland's 2-0 home loss to the Houston Astros on Tuesday night, Bauer talked and exchanged hugs with several teammates in the clubhouse before departing around 10:45 p.m. He declined to speak with reporters.

For your passion, unquenchable desire to win, and dedication to your craft ...



Thank you, @BauerOutage. pic.twitter.com/2AyaMmVsPg — Cleveland Indians (@Indians) July 31, 2019

Puig, who joined the Reds in a December trade with the Los Angeles Dodgers, was still in Tuesday night's game against the Pittsburgh Pirates as reports of the three-team trade surfaced. He ended his short stint in Cincinnati with a bang when he was involved in a benches-clearing brawl in the ninth inning and was among seven players ejected from the game.

Puig, who had to be restrained after reigniting the melee with more shouting and shoving, could face disciplinary action, including a suspension, as a result of his participation in the brawl.

"I'm going to miss all my teammates here," Puig said of the trade after the game. "This part of the year is amazing for me, being on this team and the city. Now it's time to move forward and go to my new team and help my team go to the playoffs. ... I want to say thank you to all the city, Cincinnati. We stay next door -- we're going to Cleveland."

Bauer, who is 9-8 with a 3.79 ERA and 185 strikeouts, will head to a Cincinnati team (48-56) that is seven games out of the wild card after Tuesday's 11-4 loss.

After a breakout 2018 season in which he made his first All-Star team, Bauer hasn't been as consistent as Cleveland has needed while waiting for two-time Cy Young Award winner Corey Kluber (broken arm) and Carlos Carrasco (leukemia) to return to their rotation. Kluber, who was hit by a line drive May 1, is scheduled to throw a simulated game against a group of minor leaguers Saturday and could begin a minor league rehabilitation assignment if he gets through the simulated game with no issues.

Bauer, who won't be a free agent until after the 2020 season, is making $13 million this season. In eight seasons since he broke into the majors with the Arizona Diamondbacks in 2012, he is 68-55 with 1,111 strikeouts and a 3.92 ERA.

Bauer, 28, has had his share of non-pitching issues. Earlier Tuesday, Bauer was informed that he would be fined by Major League Baseball but not suspended for firing a baseball from the mound over the center-field fence before being removed from Sunday's game against the Royals.

League Of His Own? New Reds right-hander Trevor Bauer dominated the NL in his four interleague starts this year: vs NL vs AL W-L 2-0 7-8 ERA 2.57 4.06 WHIP 1.11 1.24 Opp OPS .586 .731 -- ESPN Stats & Information

In 2016, Bauer was scratched from Game 2 of the AL Championship Series after a freak injury in which he sliced the tip of his finger while doing maintenance on his drone. He tried to start Game 3 but left after 21 pitches when the wound ripped open and caked his jersey, pants and portions of the mound in blood. He returned for the World Series.

In 2018, he traded barbs on social media with members of the Astros after insinuating that Houston pitchers were applying pine tar or some similar substance to baseballs to increase spin rate.

The additions of Puig and Reyes will give the Indians a nice upgrade offensively, particularly in the power department. They have combined for 49 home runs, 21 more than all Indians corner outfielders combined this season.

Puig is batting .252 with 22 homers and 61 RBIs, and Reyes is batting .255 with 27 homers and 46 RBIs.

ESPN's Jeff Passan and The Associated Press contributed to this report.