Billing, 22, retweeted an abusive message he had received urging him to leave the Premier League club.
The supporter told Billing: “Leave our f****** club I never want to see you in a town kit ever again you useless wanna be black donkey.”
Billing, a regular starter for Huddersfield this season, simply retweeted the taunt with a thumbs down emoji.
Huddersfield said in a statement: “We’re aware of the racist message sent to Philip Billing over social media on Tuesday evening and have subsequently referred the case to West Yorkshire Police.
“Huddersfield Town does not tolerate abuse of any kind and has a zero-tolerance stance towards any form of discrimination.
“We will give our full cooperation to the police to deal with this matter in the strongest possible way.”
Billing, a Denmark Under-21 international, has produced several outstanding displays for the Terriers this season.
His form has led to speculation of a summer move to another Premier League rival, but he was withdrawn at half-time in last Saturday’s home defeat to Bournemouth.
Town boss Jan Siewert said after the match that he was not sure whether Billing was carrying an injury or not.
The Terriers slumped to a 15th defeat in 17 league games and are 16 points from safety with eight matches remaining.
Kick It Out have condemned the abuse and have urged social media companies to do more to help safeguard their users.
“We condemn the disgraceful abuse that Philip Billing has received online and call on social media companies to take steps to act against people who use their platforms to carry it out,” Kick It Out said in a statement.
“Recent events underline that players should be protected from abuse both on and off the pitch. We are liaising with Huddersfield Town and have offered our support to Philip.”