The Welshman moved to the Santiago Bernabeu on a six-year deal at the start of the month from Tottenham Hotspur after a summer-long transfer saga.
However, Ibrahimovic thinks that Bale will immediately be expected to display his quality at the La Liga giants due to his world-record fee.
"No footballer is worth paying that amount of money for," Ibrahimovic told BBC Radio 5. "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."
Ibrahimovic has previously played for Juventus, Inter Milan, Barcelona and AC Milan.