The sportswear giant adidas has also replaced a Copacabana advert featuring the striker and betting website 888poker has dropped him as its official ambassador.
Suarez was met by outraged President Jose Mujica when he landed at a military base next to Uruguay's main airport before dawn. With his wife and other family members he was then driven to a home he has in the small coastal town of Solymar.
The 27-year-old has not spoken publicly since FIFA ruled on Thursday that he cannot play in Uruguay's next nine competitive matches, but the ban has sparked fury in Suarez's homeland and his victim has claimed he felt no anger towards him.
Chiellini said: "Now inside me there's no feelings of joy, revenge or anger against Suarez for an incident that happened on the pitch and that's done . . . I believe that the proposed formula is excessive."
FIFPro, the international players' union, also questioned the severity of the punishment, the longest ever imposed at a World Cup, which will also mean Suarez misses the start of the club season for Liverpool.
Fans queued in Rio de Janeiro to get a photo taken next to an adidas poster of a snarling Suarez where they pretended to be bitten by him, but the image has been replaced by one of Brazil right-back Dani Alves. "Adidas has decided to review all marketing activity involving Luis Suarez," said a spokesman.
Alejandro Balbi, a board member of the Uruguayan FA and Suarez's lawyer, said: "He is totally distraught. He never thought the punishment would be so severe."
Diego Maradona, the legendary Argentine, asked: "Who did Suarez kill? This is football, this is contact. They may as well handcuff him and bring him to Guantanamo directly."