The decision follows a league match in Ecuador, which resulted in Moreno being handed a 20-match ban by the national football association.
Moreno was also criticised by Italy after their defeat to South Korea at the World Cup.
To show what they think of him, he has had a row of toilets named after him in Italy.
In a statement Fifa said: "As a result of a number of controversies regarding referee Byron Moreno in Japan, Italy and South America over the past few months, Fifa has decided to launch an investigation into the affair.
"The Fifa disciplinary committee has been entrusted with dealing with the matter."
Political ambition
Moreno was suspended by the Ecuadorian Football Federation after the first division match between Liga de Quito and Barcelona of Guayquil.
After signalling six minutes of injury time in the game, he instead played 13, during which time home side Quito scored twice to win 4-3.
He also awarded two hotly-disputed penalties, sent off two players and caused confusion by first awarding a goal and then disallowing it.
Moreno is standing as a candidate in local elections in Quito next month and Barcelona president Leonardo Bohrer claimed that it was unethical for him continue refereeing in the meantime.
At the World Cup, Moreno was criticised by Italian squad members and fans after they lost 2-1 to South Korea.
Moreno awarded a debatable early penalty to South Korea, disallowed a Damiano Tomassi goal that would have won the game for Italy and then sent off striker Francesco Totti in extra time for diving.