Argentina international Higuain was sent off against his parent club in Sunday's game at San Siro following two bookable offences, having also missed a penalty.
After receiving a yellow card for a foul on Medhi Benatia, Higuain screamed in the official's face, losing his temper and earning himself a sending off.
While Juve star Cristiano Ronaldo, who scored in his side's 2-0 win over Milan, has called for leniency , the Italian Deputy PM has done no such thing.
Speaking at a press conference, Matteo Salvini, a Milan fan, said: "Football is the country’s mirror.
“I was at San Siro on Sunday and I was ashamed by the conduct of the Milan striker.
“Despite it going against my interests as a fan, I hope he’s given a long ban.”
"It seemed an unfair foul, I was fouled as far as I'm concerned. I was cautioned but I did not insult anyone," he told Milan TV.
"I apologised to the club, the fans, the coach and my companions because these episodes must be avoided.
"We are human, we feel emotions, the game was not going the right way and it was one of those days."
"At this moment he feels a lot of pressure, my words from yesterday's press conference were not by chance," he told Milan TV after his side's loss to Juve.
"Right now, he feels a huge weight on him and it shows. He must remain calm, he should apologise and assume his responsibilities.
"He has to put aside his nervousness, he is our most important player we have and he has to make the difference. He has to be clear headed."
Milan are currently sixth in Serie A, 13 points behind leaders Juve.