During the 63rd minute of the match, Arter and Hogg seemed to engage in a physical battle, during which Hogg thrust his head towards Arter and was ultimately shown a red card by referee Michael Oliver as a result.
Arter spoke about the incident following the conclusion of the game, and is quoted by Wales Online as saying: "It was heat of the battle and you sometimes get lost in that moment.
"We came face to face and I just felt there was just too much force in his head which was sore.
"I'm not sure how it looks on camera, I don't know whether or not he was pushed into me.
"He doesn't seem that sort of player but there was some force behind his push."
The incident bore a similarity to Richarlison's clash with Adam Smith during Bournemouth's match against Everton. Although Richarlison's contact with Smith was much lighter, the result was still the same, as Richarlison was shown a straight red card.
Cardiff and Huddersfield played out a 0-0 draw, leaving Cardiff without a win so far on their return to the Premier League. They are also the only side in England's top four divisions who are yet to find the back of the net this campaign.
The Welsh side will welcome Unai Emery's Arsenal to the Cardiff City Stadium next weekend, as their continue their quests for a win and a goal. Meanwhile, Huddersfield make the trip to Goodison Park to meet Everton, with both Hogg and Richarlison suspended for the match.