The former Under-17 and Under-20 coach was brought in to replace Reinaldo Rueda after last year's 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 they start their 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 June 11 when they tackle host nation Chile at Santiago's Estadio Nacional, with Mexico and Bolivia also in Group A.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.