Romo and Lindor also were fined for the incident, which occurred during Minnesota's 3-1 victory Friday night. Romo decided to serve his suspension during Saturday night's game against the Indians.
"It's disappointing, but we support Serge," Twins chief baseball officer Derek Falvey said. "We know he's a fiery guy. He's on the mound, he's always competitive, he goes out there and always lets his emotions fly. Sometimes, that's not as liked by others and sometimes, there's some jawing back and forth. That's part of professional sports, and it turned into something that was a little bit too much last night, and then the league had to hand down the discipline.''
Romo worked a perfect eighth, retiring Lindor on an inning-ending fly out. Romo and Lindor exchanged words as the shortstop ran toward first, and then the two walked toward each other before they were separated by teammates.
The Twins, Indians and Chicago White Sox are locked in a tight race for the AL Central lead. The Twins and Indians finish their weekend set on Sunday.
"The last thing we want is any type of suspension impact,'' Falvey said. "We're in a tight race here that's very likely to come down to a couple of games across probably all of the seeds in the playoff picture, and we want to give ourselves the best chance to be in the best spot at the end of the year.''
The tiff between the players predated this series.
"It's just a couple of players who continually interact with each other when they probably shouldn't," Twins manager Rocco Baldelli said after the game. "And I think it would probably be better if they didn't."
Romo's animated expressions after critical outs have rankled several opponents this season.
"If he's going to dish it, we're going to dish it back. He has to take it," acting Indians manager Sandy Alomar Jr. said.
The Associated Press contributed to this report.