The six-time Ballon d'Or winner made a game-high five key passes and 65 passes in the opposition half as Barca improved to six points in Group G.
Vieri, who won Serie A with Juve in 1996-97 and was a 49-time Italy international, lauded Messi's contribution in Turin.
"An amazing Barcelona, there was no game. They could've scored six, seven goals easy. They played fantastic," he told CBS Sports.
"Messi is a magician, he's the Harry Potter of soccer and when he stops playing, I'm throwing my TVs away. I'm not going to work no more on TV, I'm going to watch Netflix, that's it, because when he stops there's nothing else to watch."
Since Messi's first Champions League campaign in 2004-05, only Cristiano Ronaldo (38) has provided more assists in the competition than his 35.
The Argentina international helped Barca dominate as Juve – who had Merih Demiral sent off in the 85th minute – failed to record a shot on target in a Champions League home game for the first time since 2003-04 – when Opta have such data available.
Juventus forward Alvaro Morata incredibly had three goals ruled out for offside during the encounter.
Vieri was impressed by Barcelona's performance, saying: "It's just another football, another game.
"I don't know how they lost against Real Madrid, but if you see them [against Juventus] you're going to say they can't lose against anyone this year, it's impossible the way they played.
"Every game is different but the Barcelona I saw and everyone saw it's just incredible. When you've got a number 10 like that, it's just crazy.
"It's a pity there are no fans here because the fans should be seeing a team like this."
Sitting 12th in the LaLiga table, Barcelona visit Deportivo Alaves on Saturday.