The former Camp Nou forward says the Uruguay striker will be a marked man on his return from a lengthy ban - from opposition players, referees and the media
Suarez was handed a four-month ban from all football-related activity after he was found guilty by Fifa of biting Giorgio Chiellini when Uruguay faced Italy in the World Cup group stage last month.
Stoichkov, who was known for his temper during his playing days, has warned the Liverpool forward - who has been heavily linked with a move to Barca this summer - that he will now be a marked man due to his continued biting antics.
"The biting will be a problem... Because he is now marked for life," the Bulgarian, 48, told Univision TV. "Playing at Barca with what he has done is a problem.
"All opponents, referees and the media are going to make life difficult. He will have to play between provocation and media attention, which will cause a permanent tension.
"Opposing players provoke you, look for violent reactions from you, try to get you out of the game.
"They think every day you miss will be a holiday. And if you're warm-blooded... Sometimes it's hard to hold back. In addition, referees are not aware of what you say but how you react.
"Every game is a psychological war. And then there is the media... It is not easy to live like this. You have to be a bit special to live with this. What will come to Luis Suarez is going to be very hard.
"He cannot afford to do it again. But now, nevertheless, he must be positive."