The Bantams say they are working alongside Chesterfield and the Football Association following the incidents in the first half of the pre-season contest, when some City substitutes were subjected to alleged discriminatory remarks, and a spectator in the home stand subsequently left the stadium after play was suspended.
Following the game, the incident was formally reported to the match officials.
City’s chief executive officer, Ryan Sparks said: “I spoke at length last night with the players subjected to the disgusting slurs from a spectator in the home stand. We understand Derbyshire Police are investigating the situation, and we will assist accordingly.
“I would like to thank Chesterfield’s chief executive, John Croot, who has been extremely supportive since the incident. I am confident the individual will face the strongest-possible consequences, as a result of his repulsive actions.
“These events are a reminder of the amount of work that still needs to be done, in order to remove this kind of behaviour from society. There is absolutely no place for it, and we will continue to do everything in our power to protect any member of our staff from discrimination.
“Our players have our full support, and we stand shoulder to shoulder with them in collective attempts to eradicate all forms of discrimination.”