The former president of the Brazilian Football Federation represented the South American governing body on FIFA's central decision-making body.
"FIFA has taken note today of CONMEBOL's announcement that Ricardo Terra Teixeira has resigned as a member of the FIFA Executive Committee," said a FIFA statement.
"As per the FIFA Statutes (art. 30 par. 7), CONMEBOL will now have to decide immediately on the replacement of Ricardo Teixeira as one of their representatives on the FIFA Executive Committee for the remaining period of office."
CONMEBOL published a copy of Teixeira's brief resignation letter, which was addressed to the regional body's president Dr Nicolas Leoz.
In the letter, Teixeira thanks Dr Leoz, CONMEBOL executives and the presidents of South American national associations for their support during his term in office.
He cited "personal reasons" for stepping down.
Teixeira had been joined on FIFA's executive committee by fellow South Americans Leoz and Julio Grondona.
Teixeira, 64, resigned last week as head of the Brazilian Football Federation and the 2014 World Cup organising committee on health grounds.
Teixiera had been in charge of Brazilian football for 23 years but recently came under pressure to resign over allegations of corruption.
In 2001, the Brazilian Congress investigated Teixeira on suspicion of 13 crimes, including tax evasion, money laundering and misleading lawmakers, but no charges were brought.
He has also been investigated for allegedly taking kickbacks from a marketing firm that worked closely with FIFA in the 1990s.
He denied all the allegations and has never been convicted of any offence.
Teixeira could also point to the highlight of two World Cup victories, in 1994 and 2002.
Teixeira came under fire from within FIFA earlier this month, with secretary general Jerome Valcke expressing concern over the lack of progress on preparations for the 2014 World Cup.