The Spain international has warned the Welshman that the first month at his new club in particular will be a difficult time
The Spaniard recently stated that he has little doubt the former Tottenham man will eventually do well at the club, but thinks Bale will need time to get used to his new surroundings and the demands at a big club like los Blancos.
"You never know how he will adapt to a dressing-room like Madrid's with a lot of stars like Cristiano [Ronaldo] and [Karim] Benzema," Pique is quoted as saying by Sky Sports.
"Real Madrid are such an immense team - a big, big club. Everyone wants to know something about the players, about Bale too.
"When you're playing for a great team like Madrid, with a lot of pressure because you have to win every game, it's a difficult life.
"I hope he can play well, but we will see. The first month will be more difficult, then it will be a bit more relaxed."
Bale could make his official Madrid debut when they travel to Villarreal on Saturday.