The Nigeria international has deleted his account on the social networking site after receiving several abusive messages following his mistake against Juventus
The midfielder was at fault for the Italians' equaliser, as his misplaced pass allowed Fabio Quagliarella in to deny the Blues all three points in their opening Champions League Group E game.
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Chelsea wrote on Twitter: "Abuse on social networks is abhorrent. Racist tweets towards Mikel are totally unacceptable. Police informed. #CFC supports strongest action."
Two hours earlier, the Stamford Bridge side had tweeted to deny reports that the 25-year-old had been targeted through the site but have now been forced to backtrack.
The original tweet read: "Not true Mikel quit Twitter due to messages received. He'd wanted to leave for a while & deleted his acct today without looking at it. #CFC"
Mikel accepted full responsibility for his mistake after Wednesday's game, telling Sky Sports: "I'm disappointed, it was my pass and I over-hit it."