Suarez returned home to a hero's welcome in Montevideo after being kicked out of the World Cup for biting Italy defender Giorgio Chiellini.
It is the third time in four years that Suarez has been sanctioned for biting, and the latest incident triggered widespread outrage in the football world.
FIFA general secretary Jerome Valcke led calls for Suarez to seek help, brushing off suggestions the Liverpool star's four-month worldwide ban from all football activity was too severe.
Valcke told reporters: "I think he should find a way to stop doing it.
"He should go through a treatment. It is definitely wrong."
The international professional footballer's union FIFPro said FIFA should have made mandatory treatment part of its sanction.
"Luis Suarez should receive all the support he needs to deal with any off-field issues he may be experiencing at this time," said a FIFPro statement.
"This means that the focus should be on the rehabilitation and serious treatment of the player.
"FIFPro believes that treatment must be a part of any sanction."
Italy defender Chiellini expressed sympathy for Suarez and criticised FIFA's punishment, which is the heaviest ever imposed on a player during a World Cup.
"I have always considered unequivocal the disciplinary interventions by thecompetent bodies, but at the same time I believe that the proposed formula isexcessive," said Chiellini on his website.
But Valcke dismissed Chiellini's comments when told of them.
"Again, it's not just about the incident - it was seen by hundreds of millions of people," he said.
"It is not what you want your kids, the little ones who are
playing football around the world, to see in a football game at the level of the World Cup, or any level - amateur football or professional football."
Suarez, 27, bid farewell to his team mates as they prepared for Sunday's (AEST) last 16 game with Colombia. FIFA said the ban on football activities meant he could not stay at the team hotel and will not even be allowed in a stadium where Uruguay are playing during the four months.
The Uruguayan nation has rallied behind the shamed goalscorer.
A private jet carrying the player landed in Montevideo just before dawn on Friday. Hundreds of fans carrying banners with slogans such as "Luis, All Of Uruguay Is With You" were waiting.
"He has been treated worse than a murderer, when it was just a mistake," one of the fans at the airport told AFP.
President Jose Mujica said he met Suarez after his return and before the footballer was driven away to his mother's home in the southern province of Canelones.
Mujica said in his weekly radio address that FIFA's punishment of Suarez would become an "eternal shame" for football.
"We think this will be remembered, this will remain among the worst moments in the history of football. This will be an eternal shame in the story of World Cups," Mujica said.
Fallout from Suarez's ban spread quickly with gambling website 888 Poker terminating its sponsorship deal with the player.
Sports equipment giant Adidas said it was halting the use of Suarez in adverts for the duration of the World Cup. The company said it "fully" backed FIFA's ban.
British media speculated the sanctions could wipe a substantial amount off the value of Suarez if Liverpool decide to sell him. The English club has not yet commented on the case insisting it was waiting to see FIFA's report.
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