The former under-17 and under-20 coach was brought in to replace Reinaldo Rueda after last year's FIFA World Cup, initially on an interim basis.
However Luis Chiriboga, president of Ecuador's Football Federation, has opted to find an alternative for the nation before it starts its Copa America campaign in June, although Vizuete will continue to work with the organisation.
"We are looking for candidates, new options for the Copa America," Chiriboga said.
"We need to take care of this tournament and also pay attention to the qualifiers for the World Cup.
"I will not give any names. We will just make some contacts and announce our next coach in the next 30 days."
Ecuador will open the Copa America on 11 June when it tackles host nation Chile at Santiago's Estadio Nacional, with Mexico and Bolivia also in Group A.
