Saudi authorities say no charges have been filed over the incident but Usyk’s manager Alexander Krassyuk says Fury Snr should apologise.
“I had the impression that one of our guys made the headbutt and hit him with the forehead,” Krassyuk told Sky.
“Then I saw the video and it turned out to be a little bit different from my first impression.
“It would be nice if we hear some apologies from John, because this was his behaviour.
“We are the example for the whole world, a new generation of kids are taking us as an example. What will they see from this?”
Speaking to Sky Sports afterwards, Fury Snr said: “They were disrespecting my son, the best-ever heavyweight to wear a pair of boxing gloves.
“Coming out with all that rubbish, in my face, trying to be clever.
“So they stepped closer and stepped closer and at the end of it I am a warrior, that is what we do.
“If you come in the space, you are going to get what is coming.”
Son Tyson, meanwhile, said he did not see the incident and is only focused on Saturday’s fight.
“I was in the room doing interviews, but I’m not here for all that, I’m here to get the job done and go home and rest,” said the 35-year-old Briton.
WBC champion Fury and Ukraine’s Usyk, who holds the WBA, IBF and WBO belts, will fight at the Kingdom Arena with the winner becoming the first undisputed heavyweight champion of the four-belt era.
Lennox Lewis was the last undisputed champion, in 1999, when the WBC champion won the WBA and IBF titles from Evander Holyfield.