The Liverpool forward was banned on Thursday for nine international matches and suspended from any involvement in football for four months after being found guilty of biting Giorgio Chiellini in Uruguay's 1-0 win over Italy.
Suarez has now flown back to Uruguay, with Tabarez claiming that he cannot be part of an organisation that disagrees with his views on the incident.
"It is not wise or prudent to be in an organisation with people, those who exerted pressure to promote this decision and those who rendered the punishment, who managed procedures and values very different to those I have," Tabarez told reporters.
"Therefore, in the coming days, I will file my resignation to that position formally."
Uruguay face Colombia in the last 16 of the World Cup on Saturday.