Suarez faces a lengthy ban from FIFA after he apparently sank his teeth into Italy defender Giorgio Chiellini's shoulder during Uruguay's 1-0 win that saw them move into the World Cup knockout round.
Fowler refused to defend Suarez, saying a man he had seen do so much good work had again shown his ugly side.
And he fears he may now be allowed to leave Liverpool, with Real Madrid and Barcelona reportedly keen on signing him.
"You can't defend him," the former Liverpool striker said.
"Off the pitch he's an absolutely lovely fella.
"He does so much work for charity, does so much work in the community in Liverpool, and I love him as a player, but you cannot condone what he has done.
"When he gets on the pitch he just becomes a different person," Fowler told talkSPORT, admitting he was "flummoxed".
He said Liverpool fans would be saddened, having backed Suarez through two bans he served at the club, one for biting Chelsea's Branislav Ivanovic arm in a Premier League game in April 2013 and another for racially abusing Manchester United defender Patrice Evra.
"It's a real, real tough predicament most Liverpool fans are in. They love him as a player, but he's continually dragging the club's name through the mud," Fowler said.
"It's not right, especially after how they helped him last time. They tried to rehabilitate him.
"I wouldn't be surprised if he went now."
Joey Barton, the former Newcastle and Marseille midfielder who is no stranger to controversy himself, suggested Suarez's apparent bite was something which "comes with the territory" of being a winner.
Barton wrote on Twitter: "I love Suarez. I love his passion for the game... I am also aware you can't defend him here.
"All things considered I'd rather receive a bite than a leg breaking challenge.
"He's a winner. If that means he occasionally steps over the line between right and wrong, than that's what comes with the territory...
But Professional Footballers' Association chief executive Gordon Taylor said he feared Suarez's career could be brought to a premature end if he fails to control his behaviour.
Taylor -- who heads what is effectively the players' union -- worked with Suarez over the Evra affair and helped to broker a truce last summer when the Uruguayan declared his wish to leave Liverpool. He eventually stayed and scored 31 goals in a push which nearly secured the Premier League title.
Taylor said of the biting incident: "It was just so disappointing, really.
"I've been disappointed about England, but doubly disappointing when our player of the year, the Footballer Writers' player of the year and last season I thought he'd got himself back on track," he told BBC radio.
"We felt these were issues he had and offered counselling with regard to anger management.
"We've seen the best of him and that other side in just two games over in Brazil.
"Issues with regard to biting is something not normally associated with senior players in the game.
"It can't be acceptable and from that point of view there are serious issues to be dealt with and they're health issues, counselling issues, mental health issues.
"It certainly needs that to try to eradicate this from his make-up, otherwise I fear for his career."
Paul Scholes, who played nearly 500 times for Manchester United, believes a 10-match ban would not be a strong enough punishment.
He told paddypower.com that Suarez's 10-game ban for biting Ivanovic "obviously wasn't enough".
"On Tuesday night, with the biting incident... Suarez embarrassed his club, country and family.
"Banning him for the rest of the World Cup is not enough, because Colombia will beat Uruguay in their next game anyway."
Scholes thinks Suarez's behaviour will overshadow his ability as a footballer.
"He will feel terrible, and the entire incident is such a shame because he's a tremendous player," Scholes added.
"But people will remember Suarez now for his biting antics at this World Cup rather than his supreme footballing ability."
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- Luis Suarez
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