Alcaraz took the job in April this year, following Georges Leekens’ resignation in February.
He was the fourth permanent coach to take charge in 13 months.
According to reports onsuperdeporte.es, the coach who signed a contract until 2019 has returned to Spain, after bidding goodbye to his players.
Alcaraz recorded only one win in four games during his reign.
Algeria are currently bottom of Group B on just one point after five games.