The Twitter message, which we will not repeat, was posted in response to Tshimanga scoring his second penalty in the 2-1 win against Dagenham and Redbridge on Saturday.
Many Spireites fans, including the Derbyshire Times, reported the offending tweet to Twitter and requested it be removed.
Chesterfield FC said: “We are aware of a social media message with racist overtones, posted in a reply to one of our tweets, which has been reported to the police. Derbyshire Police are now investigating the matter.”
And Derbyshire Police said: “The post has been removed. Please do not retweet screenshot. The incident will now be investigated. Racism has no place in society.”
Police have been praised for their quick response.
Tshimanga took his tally this season to 23 goals in 25 league games with a brace against Dagenham, scoring from the penalty spot in each half.