Bale left Spurs for the Spanish club for a reported fee of €100million (£85.3m), bringing one of the transfer window's longest-running sagas to a conclusion.
The Wales international has described the switch as a "dream", but Paris Saint-Germain striker Ibrahimovic, who left Inter to join Real's arch rivals Barcelona in 2009 in a transfer believed to worth €69m, believes Bale could face hostility if he does not meet the high standards of the Real fans.
"No footballer is worth paying that amount of money for," Ibrahimovic told BBC Sport.
"There is a lot of pressure on him.
"I know that when Zinedine Zidane played for Madrid, the fans were whistling against him.
"If they can whistle against Zidane, for me one of the best players in history, I hope Bale has a lot of patience.
"I had a dream to come to Barcelona, but afterwards I am thinking that maybe you should keep your dreams, instead of making it come true.
"Bale's move is similar to my transfer to Barcelona, but what creates that situation and the fee is the media, the selling club and how desperate the buying club are to buy a big name."
Ibrahimovic has won league titles in the Netherlands, Italy, Spain and France, but does not picture himself playing in England at this stage in his career.
"To come to England? My time has passed," Ibrahimovic added.
"I am above 30, I have a good relationship with PSG, with the team. I feel that I can bring out all my qualities at PSG. I have a big responsibility also at PSG. So in my mind, no.
"But then you never know what happens in football. When I went to Barcelona, I was living my dream.
"In my head I was there for five years. In the end I was there for only one. So every time I plan my future, I change it. So better to take one day at a time."
