Eddie McKay, 58, was with his son when he was attacked by seven or eight thugs wearing balaclavas around midnight on Monday.
Mr McKay suffered injuries to his back and arms.
His daughter Rachel confirmed her father, from Newcastle, was recovering in hospital but wanted to warn other fans out in Milan.
She told Sky News: “My dad is stable and in a bit of shock.
“He’s gutted he’s missing the match, but just wants every other Newcastle fan out here to be aware and be safe.
“He has just had two knee replacements, so he fell when he was being chased and that is when he was attacked.
“My brother is okay, but is in shock after seeing that happen to our dad. I’m flying out there later. We haven’t slept all night.”
Mr McKay’s family will be flying to Milan later on Tuesday to be by his side.
Pictures posted online showed a man with a bloodied torso lying on the ground.
The motive behind the stabbing in the city centre neighbourhood of Navigli is not currently known and nothing was stolen.
Reports on social media claimed other Magpies fans were heading back to their hotel from an area where fans had gathered before being jumped from behind and attacked with knives.
Italian police say they are currently investigating whether it was a football-related attack.
A spokesperson for Milan Police said: “The incident took place about midnight in the neighbourhood of Navigli which is populated with bars.
“A police patrol came across the incident, which involved seven or eight people wearing hooded sweatshirts. We are still searching for these people.
“A supporter of Newcastle, who is 58 years old, suffered two slight wounds to his arms and one a little bit deeper on his back. He was sent to the Policlinico Hospital and is expected to be discharged later today.
“DIGOS (Divisione Investigazioni Generali e Operazioni Speciali), the branch which deals with football supporters, is investigating, but at this moment it is not clear if this is related to football or something else because no emblems were visible.”
Newcastle United said: “We are deeply concerned by reports that a supporter was seriously assaulted in Milan on Monday evening and we are liaising with local authorities to understand the circumstances.
“Our thoughts are with the supporter and his family and we hope for a full and speedy recovering.”
Around 5,000 Newcastle fans have flocked to the Italian city to cheer on Eddie Howe’s side in their match against AC Milan at the iconic San Siro stadium.
It is the Toon Army’s first Champions League game in 20 years.