The supporter, a British national, was stabbed in the arm and back in the attack in the Navigli district of the city, a canalside area known for its nightlife.
The back wound was the most serious but the victim is expected to be released from the Policlinco hospital in the coming hours, a police spokesperson said.
He was with a friend when a group of seven or eight people, their faces covered by hoods, attacked him at about midnight on Monday.
In a statement to British media, Newcastle said they were "deeply concerned" with the reports of the stabbing.
"We are liaising with local authorities to understand the circumstances. Our thoughts are with the supporter and their family and we hope for a full and speedy recovery," the statement added.
Milan declined to comment.
Newcastle face seven-time European Cup winners Milan in Group F at San Siro later on Tuesday. The English side are back in Europe's top club competition after a 20-year absence.