Later in the day on Wednesday, the Reds placed Mesoraco on the seven-day disabled list with a concussion.
Mesoraco, who was also fined an undisclosed sum of money, is appealing the suspension.
"Part of the reason I'm appealing is because I want to appeal. That's really the only reason," Mesoraco said before he was placed on the DL. "There's really nothing else for me to say."
During the third inning of Monday's 11-5 loss to the Padres, Mesoraco was ejected by Fairchild for arguing balls and strikes. The exchange became heated and Mesoraco made contact with Fairchild as he was being restrained by manager Dusty Baker.
Mesoraco, a 24-year-old rookie, felt he was sticking up for his pitching staff.
"I was frustrated and I let my emotions get the best of me," Mesoraco said. "At the end of the day, I was doing it for my team.
"You're supposed to stick up for them, not stick out for them. He's learning," Baker said. "Unfortunately, we couldn't get there in time to prohibit him. I let him go because I thought it was over."
In the second inning of Monday's game, Mesoraco was involved in a hard home plate collision with Cameron Maybin. Mesoraco was back in the starting lineup on Tuesday for a 7-6 win over San Diego, but left before the seventh inning because of dizziness from being overheated.
"He was a little starry-eyed the last couple of days," Reds manager Dusty Baker said. "We weren't sure exactly what we were going to do. That was a heck of a collision at that plate."
The Reds purchased the contract of catcher Dioner Navarro from Triple-A Louisville to replace Mesoraco. To make room for Navarro on the 40-man roster, first baseman Mike Costanzo was designated for assignment. Navarro was batting .330 with four home runs and 27 RBIs in 57 games with Louisville.
It could take up to two weeks for MLB to rule on Mesoraco's appeal.
If Mesoraco is suspended, Baker said there would be no thought of trying to get by with only Ryan Hanigan at catcher.
"It's hard to go with one catcher. It's hard enough to go with two," Baker said.
Mesoraco entered Wednesday's game batting .221 with five home runs and 14 RBIs in 46 games.
"Whatever happens, I just want the least amount to hurt the team," Mesoraco said. "They can do whatever they want, but it comes down to me not wanting to hurt the team."