Johnson chose to have a haircut and went on to win the match. A video of a trainer cutting Johnson's hair was tweeted by a local reporter and went viral.
The Division on Civil Rights of the New Jersey attorney general's office is now investigating the incident.
Cappuccio spoke of the video Wednesday.
"We have viewed the video footage that has gone viral and are deeply troubled by the embarrassment and humiliation our young student athlete endured," he said. "District administration has been working diligently around the clock for the past several days collecting as much info as possible about the sequence of events occurring this past December 19."
Johnson family attorney Dominic Speziali addressed the board Wednesday, and said Johnson and his family are supportive of the coaching staff and the trainer who cut his hair.
"The blame here is on the referee," Speziali said. "It's still not clear to me why that had to happen, in that manner, to Andrew."
Cappuccio noted that Maloney isn't employed by the school district, and therefore the board "has no control as to the extent to which he will be able to continue to work as a wrestling official."
However, the New Jersey State Interscholastic Athletic Association said in a statement Monday that Maloney wouldn't be assigned to referee any event "until this matter has been thoroughly reviewed."
Maloney was accused of using a racial slur against a fellow referee during a 2016 social gathering. In that incident, Maloney told the Courier-Post of Camden, he didn't remember using the slur, but believed the eyewitness accounts of those saying he did.
Maloney hasn't responded to media requests for comment.