The Scottish international was the subject of abuse that was brought to the club's attention through a social media video.
The video showed an individual at the club's Stamford Bridge stadium hurling sectarian abuse at McGinn.
"We are aware of a video circulating on social media showing an individual using abusive language of a sectarian nature in the crowd at Stamford Bridge on Saturday," Chelsea said.
"Chelsea Football Club finds all forms of discriminatory behaviour totally unacceptable and we condemn the language used.
"The club is working to identify the person involved and will take the strongest possible action against them."
Aston Villa added: "Aston Villa are grateful to our friends at Chelsea FC for their swift and decisive action in both condemning the bigotry aimed at John McGinn at Stamford Bridge and in launching an investigation to identify the culprit.
"Aston Villa will fully support that investigation. Both clubs have zero tolerance for the scourge of discrimination in any form when it occurs in our stadia."
"Heading there now for tomorrow's game and will talk to the club. You get vile abuse from many fans of many clubs, but this is NO excuse! I hope and expect investigations!"
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