Borussia Mönchengladbach forward Jordan was racially abused on social media after Tuesday's German Cup quarter-final defeat to third division Saarbrücken, the Bundesliga side said on Wednesday.
"Disappointment and criticism are understandable reactions to losing a game. Hate, insults and racism are not and never will be," a statement said.
United States forward Jordan is on loan from Union Berlin.
On Monday, the 36 clubs in the top two German tiers announced a campaign for this weekend's matchday entitled: "Together! Stop hate. Be a team."
The campaign will coincide with the International Weeks against Racism from March 11 to 24.