Hader had several of his tweets from 2011 and 2012 exposed.
"During last night's game, we became aware of Mr. Hader's unacceptable social media comments in years past and have since been in communication with the Brewers regarding our shared concerns", Major League Baseball said in a statement.
After the game, the 24-year-old apologized for what he had posted online prior to being drafted in the 2012 amateur draft.
'Being 17 years old, you make stupid decisions and mistakes, ' Hader said. "We'll talk more on the plane (Wednesday)", said Brewers teammate Lorenzo Cain, who is black, USA Today reporter Gabe Lacques tweeted.
Hader's Twitter account since has been deleted and Brewers general manager David Stearns issued his own statement regarding the pitcher, saying he's been a good teammate.
Hader, who grew up in Millersville, Maryland, outside the state capital of Annapolis, apologized when he spoke to reporters after the All-Star Game.
Jason Roy faces fitness test ahead of England's ODI decider with India
Considering England's ascendancy in white-ball cricket since 2015, the equation has balanced out over the last two encounters. I stuck to the basics and stuck wicket-to-wicket. "Luckily, over the past year we've managed these situations really well".
"His comments are inexcusable, and he is taking full responsibility for the consequences of his actions", the statement said. It won't happen again. What did Josh Hader say on Twitter? "I was just trying to understand the situation", Cain said. For me, I'm moving on from it. I'm deeply sorry for what I've said.
If you think making Hader do such things is "punishment", well, that opens up another conversation altogether I suppose. They even occurred before Major League Baseball had a formal social media policy.
"We all said some insane stuff when we're young", Cain told reporters after the game.
"I'm completely and utterly embarrassed and feel awful to have put the fans, my teammates and the Blue Jays organizion in this position". 'I really don't know exactly what's all out there'. Like I said, we'll move on from it. So I'm fine. Everybody will be OK. "So we move on from it".
Tom Hader, the player's father, was among a dozen family members who were waiting outside the National League clubhouse following the game and all were still wearing replica jerseys that had the name Hader on the back.