The Spanish Federation (RFEF) announced on Thursday that he would be replaced by the current under-21 national coach Luis de la Fuente.
Spain were eliminated on penalties in Tuesday's contest, which finished goalless after extra-time at Education City Stadium.
Former Barcelona boss Enrique's contract was due to expire at the end of the tournament in Qatar, and it was confirmed on Thursday he will not be staying on.
"The RFEF would like to thank Luis Enrique and his entire coaching staff at the helm of the absolute national team in recent years," the statement read.
"The sports management of the RFEF has transferred to the president a report in which it is determined that a new project should start for the Spanish soccer team.
"The aim is to continue with the growth achieved in recent years thanks to the work carried out by Luis Enrique and their collaborators."
Luis Enrique had been in charge of Spain since 2018, bar a four-month period in 2019 when stepping aside due to the illness and subsequent death of his young daughter.
He led La Roja to the semi-finals of Euro 2020 last year, where they lost on penalties to Italy, and to the 2020-21 Nations League final, where they were beaten by France.
Spain's loss to Morocco was their third straight tournament exit on penalties, having also suffered defeat by that method against hosts Russia in the 2018 World Cup last 16.
The RFEF confirmed Enrique would be succeeded by de la Fuente, who's coached a number of Spain's youth sides in recent years. He will officially take charge next Monday.
De la Fuente, 61, joined the RFEF in 2013 as the under-15 manager having worked with players like Marco Asensio, goalkeeper Unai Simon, Eric Garcia, Pau Torres, Pedri, Carlos Soler and Dani Olmo when they were youngsters.
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