He told Sky Sports 1 "He got a seven-game ban at Ajax for doing the same thing. He obviously has a real problem.
"There is that madness-genius gene in him because as a player, you hold your hands up - he's exceptional with people talking about him being player of the year, but what he did today, is indefensible.
"Even the staunchest Liverpool supporters cannot look at that and think that's alright.
"You can't defend that and anyone who tries to is completely wrong, because the club is bigger than any player who has been on the football field.
"What's he doing? Why on earth would you want to take a chunk out of someone's arm when you are on a football field?
"That is an absolutely incredible act of brutality. It's madness."
Redknapp also believes Suarez should face a sizeable suspension.
He said: "I'd be surprised if he plays again this season. What message does will that send if he doesn't get a two or three-game ban.
"He's letting the club down."
Regarding the Uruguayan's long-term future at Anfield, Redknapp said: "He's giving the owners a problem.
"It's such a shame because he's playing for such a great football club. How many more chances are you going to give him?
"I wouldn't be surprised if he's still here (next season). I wouldn't think that's the end of him at Liverpool football club.
"It's not the first time now but footballers are valuable commodities, they certainly aren't going to sack him for that, the only thing maybe is they will sell him in the summer as they think it's one time too many now."
Professional Footballers' Association chief Gordon Taylor was disappointed Suarez's actions spoilt a good game of football.
While Taylor was coy over whether he would support a punishment, he expressed his disgust with the Liverpool forward.
"It was not good to see to say the least. It was unacceptable," he said on Sky Sports News.
"His reputation for controversy continues to increase when he can be such a good player, one of the world's best, so it is a real dilemma now.
"It's uncalled for, it's not good, it's depressing, it's such a shame for a player who's a really good footballer but this is not the first time that such things have happened.
"I know it's a really difficult one for Liverpool and the FA are going to have to deal with it.
"There's physical contact, emotions run high but no matter what players these days have to be considered as role models for youngsters.
"It was such a good game, great comeback, but this will take all the headlines."
Taylor admits his worry that Suarez is not learning from his controversial mistakes.
"It doesn't make it better when things have happened before and they're repeated again," he added.
"You begin to wonder 'is he going to learn his lesson? Because when his football shines through he's so highly regarded so it's just a big shame."