Edwards was optioned to Triple-A Iowa after he had trouble with his motion and got off to a tough start this season. Lee Long, Edwards' agent, said the messages came from a couple different people.
"I've known CJ for a long time and while he has mentioned being upset at social-media attacks in the past, the recent incidents are completely beyond normal fan frustration," Long said Tuesday in a statement. "No player should be expected to bear such personal attacks especially based on the color of their skin."
Theo Epstein, the president of baseball operations for the Cubs, condemned the content of the messages and said the club supports Major League Baseball's investigation, which was first reported by The Athletic.
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"In a sport that celebrates diversity and unites people from all backgrounds, we are appalled anyone claiming to be a fan would send divisive and bigoted insults to a player," Epstein said in a statement. "Whether spoken, posted or published, this type of reprehensible language and views cannot be tolerated in our game or society."
The 27-year-old Edwards, who is African American, declined comment through a spokeswoman for the Iowa Cubs.
Edwards was selected by Texas in the 48th round of the 2011 draft. The wiry right-hander was traded to Chicago in the July 2013 that moved Matt Garza to the Rangers. Edwards helped the Cubs win the World Series in 2016. He went 3-2 with a career-low 2.60 ERA in 58 games last year.
Long said in his statement they appreciate the work by the Cubs, Major League Baseball and the players' union in addressing the messages. He also said Edwards appreciates all the support he gets from Cubs fans.