Hawks forward Chol, who is of South Sudanese heritage, posted a screenshot of the comments he received on Instagram following his side's loss to the Western Bulldogs on Friday night.
"You can talk shit all you want but don't be like this guy," Chol wrote in his caption.
Chol kicked an equal game-high three goals for Hawthorn in their 12.5 (77) to 9.17 (71) loss at the MCG.
The 29-year-old former Gold Coast and Richmond forward has been the victim of racist abuse on multiple occasions throughout his decade-long AFL career.
On Saturday, the Hawks and the AFL integrity unit confirmed they are working together to investigate the latest incident.
If identified, the perpetrator faces being banned from attending AFL matches.
"Racism has no place anywhere, anytime - not in our game, not in the community and not online," Dillon said in a statement.
"Players, or anyone, should never be subjected to this sort of abuse.
"To be clear, if you think this behaviour is acceptable, then you are not welcome in our game.
"Mabior's courage to call this out should be commended and our immediate focus is supporting him and the Hawthorn Football Club."
Hawthorn CEO Ash Klein said racist behaviour is "simply not acceptable" and expressed the club's support for Chol.
"There is no place for racism in our game and in our society," Klein said in a statement.
"If you are the sort of person who thinks it's OK to make a comment or send a message like this, we don't want you as part of our game.
"We commend Mabior's courage in calling this out and we stand with him.
"Our immediate focus is on wrapping our arms around and supporting Mabior."
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