The Spaniard, who previously led Paris St-Germain to the French league title and won three Europa Leagues with Sevilla, was appointed Gunners boss in May 2018, succeeding Arsene Wenger.
He has been replaced on a temporary basis by assistant and former Arsenal midfielder Freddie Ljungberg.
Arsenal said the decision had been “taken due to results and performances not being at the level required”.
The Gunners have not won in seven games and lost 2-1 at home to Eintracht Frankfurt in the Europa League on Thursday.
It is their worst competitive run without a victory since February 1992, which was eight games under George Graham.
They are without a Premier League victory since 6 October and eight points off the top four.
Ljungberg took training on Friday and the Arsenal statement added: “We have full confidence in Freddie to take us forward.
“The search for a new head coach is under way and we will make a further announcement when that process is complete.”