West Yorkshire Police arrested a 16-year-old boy on Wednesday for sending the abusive message to Billing.
Posting a private message to Billing’s Instagram account, the supporter wrote: “Leave our f*****g club I never want to see you in a town kit ever again you useless wannabe black donkey.”
The 22-year-old responded by tweeting a screenshot of the racist taunt with a thumbs down emoji.
Billing has made 26 Premier League appearances for Huddersfield in a difficult season for the club, who are bottom of the table and 16 points from safety with just eight games left.
He was withdrawn at half-time in last Saturday’s home loss to Bournemouth, with Siewert saying after the match that he was not sure whether Billing was carrying an injury or not.
Speaking on Thursday, Siewert condemned the abuse and insisted Billing wouldn’t let it affect him.
“First of all I can say we as a club, and me personally, we don’t tolerate something like this. This is unacceptable for me,” Siewert said.
“This is a brainless comment. Racism should not be tolerated and I can’t believe something like this still happens today.
“I spoke to Philip this morning and he is fine. He trained also today and we spoke about it and I back him.
“But we shouldn’t talk about this because it gives these people a platform. We should talk about the people who are exceptional in this country.
“We’re talking about one per cent instead of 99 per cent. Let’s talk about the 99 per cent and not of someone like this.”
Siewert said he did not know whether the incident was likely to force Billing to consider his future at the club.
But he insisted the former Esbjerg midfielder, who joined Huddersfield in 2014, would be available for selection in Saturday’s league game at West Ham.
“I don’t know. For me I was just talking to him about how he feels at the moment. I asked him if he was able to train and he said ‘yes, of course I’m able to train’,” Siewert added.