Bradford ran out 1-0 winners in the game thanks to Romain Vincelot's header, but striker Clarke-Harris took to Twitter following the clash to express his disappointment at an alleged incident that took place during his post-match warm-down.
His Tweet read: "To that one Bradford fan doing monkey chants at me as I was doing my runs at the end of the game you should be disappointed in yourself."
Rotherham released a statement saying that Bradford has contacted the police about the alleged incident and that an investigation was underway.
That statement read: "Rotherham United have been made aware of an allegation of racial abuse towards one of our players from a home area of the ground after the game against Bradford City at the weekend.
"Like ourselves, our friends at Bradford City do not tolerate any form of discrimination, and as such we have been informed that the allegation has been passed onto the police and is now under investigation.
"Rotherham United operate a zero-tolerance policy on discrimination of any kind, and will fully assist with any ongoing investigation into the incident."
Bradford followed that up with a statement of their own in which they confirmed that they had appologised to the player and to Rotherham for the incident.
"The Club have been given a first name for the individual believed to be involved and also have CCTV footage of the incident.
"We will work closely with Rotherham United and the West Yorkshire Police to continue the investigation into this incident, confirm the individual involved and take appropriate action.
"The Club have issued an apology to Rotherham United and to the player in question after the game on Saturday, but we would like to once again apologise for any distress and offence caused by the incident."
To that one Bradford fan doing monkey chants at me as I was doing my runs at the end off the game you should be disappointed in yourself
— jonson clarke-harris (@ClarkeHarris) 16 de septiembre de 2017