The Terriers have confirmed there were two separate complaints made to the club after their game against Leeds last Saturday and West Yorkshire Police confirmed they were investigating the claims, but nothing had been brought to their attention during the match.
Huddersfield communications manager David Sykes said: "We have had two separate complaints and are obviously taking the complaint very seriously.
"We will help West Yorkshire Police in any way we can with their enquiries in order to get to the bottom of the matter and we are also investigating the allegations thoroughly."
Superintendent Dave Lunn said the police would be looking at whether any racial chanting took place, but added: "This was a successful policing operation of a local derby, which saw only four arrests for public order offences.
"Our priority was around achieving a safe and enjoyable match for all those attending, both prior to and following the event.
"We worked closely with the club to achieve this outcome. I would therefore like to thank the fans for their behaviour throughout, in particular their patience in relation to exit arrangements from the ground."