Former Sevilla and Espanyol boss Machin leaves just months after joining last November with Elche already in the relegation zone.
"Pablo Machin will not continue as coach of the first team," the club said in a statement.
Elche only ended their wait for a first league victory of the season last month after failing to win any of their opening 19 games.
Machin's side had taken four points from their two previous matches before Sunday's loss to Sociedad.
He is the third coach to be sacked by Elche this term, following the dismissals of Francisco Rodriguez and Jorge Almiron.