While Kane has scored four goals already in the Bundesliga and Bayern are level on points with the leaders, United have lost three of their opening five games, including last weekend's 3-1 home reverse against Brighton and Hove Albion.
United manager Erik ten Hag is already under scrutiny and things could get a lot more uncomfortable for the Dutchman if they suffer defeat against the six-time European champions in one of the standout fixtures of the opening week.
Kane, who played in five Champions League campaigns with Tottenham Hotspur before signing for Bayern in the close season, said underestimating United would be dangerous.
"They've been going through a tough spell recently but sometimes that can make a team dangerous because they want to respond," Kane, who was reportedly a target for Manchester United, told reporters on Tuesday.
"We're at home and want to control the game but we need to be careful of their threat. I don't think about form because every game can be different. There can be big response from teams going through a difficult spell."
Kane believes the defender has been treated badly.
"I think H has come under some unnecessary scrutiny," the striker said. "He has probably been scapegoated a bit.
"He is a really good friend of mine, a great guy and a really hard working professional. He has been one of England's best defenders over recent times and in England's history."
Kane said he was delighted to see Spurs start the season strongly but added that his only focus now was winning trophies with Bayern Munich and helping them to European glory again.
They last won the Champions League in 2020 against a Paris St Germain side managed by current Bayern boss Thomas Tuchel.
"Time will tell. For sure there is a reason Bayern brought me here," Kane said. "They are eager to get back to winning the Champions League. They feel I can be a big help and I feel like I can help as well. We have to focus on the group stage."
Tuchel, who took Chelsea to the Champions League title in 2021, described Kane as a "difference maker".
"In time he will make players around him better and will learn how to make them shine. He will assist and not only score. He will be the difference and he's already the difference," Tuchel, who will serve a touchline ban on Wednesday, said.
"He is very important and that's why we relied heavily on this transfer and I'm 100% convinced he will prove us right."
Tuchel, who was sacked by Chelsea last year, has some sympathy for United's current plight ahead of the Group A game.
"There's always a lot of noise around Man United. A lot of pundits in the UK are (ex-players) from Manchester United. You've a legacy from (their former manager) Alex Ferguson which creates expectations," he said.
"We can never be sure about Manchester United and we need to control the game. They can be very dangerous."