High-profile figures from across the world of sport have called for the striker to seek expert help over his persistent indiscipline
Suarez has received a nine-game suspension and a four-month ban from all football-related activity for biting the Juventus star during Uruguay’s 1-0 victory over Italy in Group D.
The Celeste won the match and sealed their route to the last 16, but will be without Suarez for the rest of the tournament following his sanction.
“He should go for treatment," Valcke told reporters.
"It was seen by hundreds of millions of people. It is not what you want your kids, what you want the little (ones) who are playing football around the world, to see at a World Cup.
"It is not Liverpool who is punished. It is the player who is punished and what he did has not only happened in international games.
"So the Disciplinary Committee took into consideration the past events and the past behaviour of Luis Suarez and that is why they made their decisions."
Suarez has already been involved in biting controversies on two previous occasions, having been banned for seven matches in 2010 for gnawing on PSV's Otman Bakkal during his time at Ajax.
Most recently, he was suspended for a further 10 games after biting Chelsea’s Branislav Ivanovic while on duty for Liverpool in the Premier League.
International players’ union FifPro have also called for Suarez to “receive all the support he needs”.
A statement from the organisation read: "The focus should be on the rehabilitation and serious treatment of the player. FifPro believes that treatment must be a part of any sanction."
Suarez, for his part, has denied the allegations, suggesting that the altercation with Cheillini was little more than a coming together between the two men.
The striker has flown back to Montevideo, while his team-mates are preparing to face Colombia at the Maracana on Saturday.