Marimo's departure on Friday came before Zimbabwe's first group phase match away against Gabon in Libreville next week.
Marimo told officials he was not prepared to work with a foreign adviser unless it was a high-profile coach from an established footballing nation like Brazil, England or Germany. He was also angry over plans to replace his two assistants.
Speculation over the appointment of an adviser from neighbouring South Africa has dominated the local press.
Zimbabwe Football association chairman Rafique Khan said he was hoping to meet Marimo on Sunday to persuade him to change his mind.
Marimo, a former captain of the national team, steered Zimbabwe to the African Nations Cup finals for the first time last year. The other teams in Zimbabwe's World Cup qualifying group are Nigeria, Algeria, Angola and Rwanda.
