Union spokesman Greg Bouris confirmed the appeal and said the players' association had no further comment.
Rodriguez, who was back at third base and batting third for the New York Yankees against the Chicago White Sox on Wednesday night, said he had "no reaction" to the filing of the grievance.
"I don't think any of us thought it was going to be any different," Yankees manager Joe Girardi said. "As far as having a reaction, it's kind of what I expected. It's part of the process that was negotiated between MLB and the players' association and you let it play out. I expect him to play a lot. We need him to help us."
Major League Baseball declined comment.
Rodriguez was suspended through the 2014 season on Monday when the league penalized 13 players following an investigation into Biogenesis of America, a shuttled Florida anti-aging clinic accused of distributing banned performance-enhancing drugs.
The other 12 players accepted 50-game suspensions, but Rodriguez said he planned to fight. Union head Michael Weiner said the punishment for the slugger was "way out of line."
Under the collective bargaining and joint drug agreements, discipline must meet a "just cause" standard.
Rodriguez's punishment was scheduled to begin Thursday, but he is allowed to keep playing until the grievance is heard by arbitrator Fredric Horowitz. He isn't expected to rule until November or December at the earliest.
Coming back from hip surgery in January, Rodriguez played his first game of the season Monday night in the series opener at Chicago. The three-time AL MVP singled in his first at-bat and was 2 for 6 with a walk in his first two games.
He followed that up by going 1 for 5 with a single and walk on Wednesday.
The 38-year-old Rodriguez has been booed lustily since his return, except for when he was hit by a pitch in the third inning of the Yankees' 3-2 loss Tuesday night.
The Yankees are off Thursday and then open a three-game series against AL Central-leading Detroit on Friday night in New York. It will be the first home game for Rodriguez since the suspension was announced.
"I am curious what it's going to be like Friday," Girardi said. "I'm not sure. And I don't really know what the appropriate response is. I don't think it's my right to tell people how to respond certain situations."
Asked how he expects to be received, Rodriguez said, "I'm not sure."
How would he like the crowd to react?
"Same way you would like them," Rodriguez said. "Again, I'm just super excited to come home, put on the pinstripes and play for the greatest fans in baseball."
Rodriguez, who agreed to a 10-year, $275 million contract with the Yankees in December 2007, is the majors' active leader with 647 career homers. He helped New York win the 2009 World Series, batting .365 with six homers and 18 RBIs in the post-season that year.
In an interview on MLB Network Radio on Sirius XM, former teammate Johnny Damon said Wednesday that title would be diminished if Rodriguez used performance-enhancing drugs during the playoff run.
"I really haven't gotten to think that far, but if that's how he was able to hit in the post-season, like he did that year, then yeah, absolutely," said Damon, who has been friends with Rodriguez since they were teenagers. "Then you start going and saying, 'Well, was anybody on their team cheating?'
"There's just so many different factors that determine if a team wins, and A-Rod was a huge determining factor."
Asked about Damon's comments, Rodriguez said he hadn't seen what he had said.
"I talk to Johnny all the time so no disappointment whatsoever," Rodriguez said.
AP Sports Writer Andrew Seligman contributed to this report.
Jay Cohen can be reached at http://www.twitter.com/jcohenap