The top four teams qualify for the World Cup while the fifth-placed side can make it to Russia if they win a home-and-away playoff against New Zealand.
Celico is to take over on an interim basis, the Ecuadorian Football Federation said in a statement on Wednesday.
His first responsibility will be to prepare the team for the final two qualifiers against Chile in Santiago and Argentina at home in Quito next month.
Ecuador can still qualify for next year's tournament in Russia if they win both matches and other results go their way.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Ian Ransom)
