The Liverpool striker allegedly bit Italy defender Giorgio Chiellini while representing Uruguay on Tuesday, with the Juventus man seeming to show the referee bite marks on his shoulder after the incident.
Scholes feels that suspending the forward for the remainder of the World Cup is not an option as well as feeling that the 27-year-old has tainted the memories supporters will have of his career.
"Suarez embarrassed his club, country and family,” he told Paddy Power. "Banning him for the rest of the World Cup is not enough, because Colombia will beat Uruguay in their next game anyway.
"He will feel terrible, and the entire incident is such a shame because he’s a tremendous player. But people will remember Suarez now for his biting antics at this World Cup rather than his supreme footballing ability."
Scholes also commented that the 10-match ban that Suarez received for biting Branislav Ivanovic in 2013 "obviously wasn't enough."