The club said in a statement that reserve team coach Cristobal Parralo would take charge of training while a successor for Garitano is found.
According to local media reports, former West Bromwich Albion and Real Betis coach Pepe Mel is the front runner to get the job, while ex-Deportivo player and Espanyol manager Sergio Gonzalez has also been mentioned as a possible candidate.
Garitano rose to prominence in Spain by leading tiny outfit Eibar to back-to-back promotions although in 2015 he resigned from the club he used to play for at the end of their first season in the top flight. They were relegated but later reinstated after Elche's administrative relegation.
He then took over at Valladolid in the Segunda Division A in the summer of 2015 but was sacked little more than two months into the new season.
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(Reporting by Richard Martin, editing by Neil Robinson)
