Ecuador had faced possible expulsion from the tournament after Chile complained they had fielded an ineligible player during the qualifiers.
They were fined and received a points deduction for the next World Cup qualifiers but have been allowed to compete in Qatar.
The player, Byron Castillo, was left out of the squad to avoid further controversy.
At Ecuador's opening game against Qatar, to kick off the World Cup on Sunday, some among their massed ranks of yellow-clad fans sang a homophobic chant against Chileans.
"The FIFA Disciplinary Committee has opened proceedings against the Ecuadorean Football Association due to chants by Ecuadorean supporters," world football's governing body said in a statement late on Tuesday, citing article 13 of its disciplinary code.
Potential sanctions in the code include playing a match without spectators or a ban on playing in a particular stadium.
There was no immediate response from Ecuador's football federation. It has been exultantly re-tweeting images from their 2-0 win at the Al Bayt stadium.
Much to the amusement of many watching around the world, Ecuador fans also chanted "We want beer!" in reference to a controversial stadium ban on alcohol consumption at the insistence of the conservative Muslim host nation.
LGBT rights have taken prominence during this World Cup, drawing some protests, as homosexuality is illegal in Qatar.
Ecuador are joint top of Group A with the Netherlands whom they face on Friday.
