It was in response to the MLBUA calling Machado's ban for making contact with an umpire during San Diego's game Saturday against the Colorado Rockies a "slap in the face."
"One game..one single game. What kind of precedent is that setting? It is NOT okay to throw a temper tantrum and physically touch someone of authority, just because you don't agree. Violence in all workplaces is not tolerated. Period," the MLBUA said in its Facebook post Tuesday.
The MLBUA went on to call the suspension a "disgrace" and said any physical contact with an umpire cannot be tolerated.
"Major League Baseball has to always lead by example in all cases of violent behavior, on and off the field," the MLBUA wrote. "With that being said, the MLBUA is extraordinarily disappointed in Major League Baseball for its disciplinary 'inaction' handed down to Manny Machado."
The post was accompanied by a string of hashtags: #Disappointed, #LeadByExample, #NotAppreciated, #Violence, #TemperTantrum, #Inaction, #NotTolerated, #MakeanExampleof, #OneGameSuspension, #RepeatOffender and #Nonsense.
MLB said the punishment, imposed Monday by chief baseball officer Joe Torre, was for "aggressively arguing and making contact'' with plate umpire Bill Welke.
"Mr. Machado is appealing his suspension and we do not believe it is appropriate for the union representing Major League Umpires to comment on the discipline of players represented by the [Major League Baseball] Players Association, just as it would not be appropriate for the Players Association to comment on disciplinary decisions made with respect to umpires," MLB said in its statement later Tuesday. "We also believe it is inappropriate to compare this incident to the extraordinarily serious issue of workplace violence."
Machado denied that he made contact with the umpire.
"Honestly, you know, I'm just waiting for my appeal, waiting for MLB and Joe Torre to get back to me. Honestly just waiting for my hearing to plead my case, and that's all we're going to worry about,'' Machado said before Tuesday night's game against Milwaukee. "I've got MLB and the Padres and ownership behind me on this. We're just all on the same page and we're going to move forward from this.''
Machado declined comment when asked if he thought the umpires' social media posts were unprofessional. He chuckled when asked if he felt he was being targeted.
"Honestly, baseball's been going on for a lot of years, been going on for a hundred some years and it's going to continue to keep going and we go out there and we play baseball and we enjoy ourselves every day,'' he responded. "At this point, we're just waiting for my hearing. MLB put something in place to handle things like this.''
Machado, 26, is batting .264 with 14 home runs and 40 RBIs for the Padres after signing a $300 million, 10-year contract in spring training.
Information from The Associated Press was used in this report.