The 52-year-old took charge in February 2011 following the dismissal of Jose Antonio Camacho, and helped the Basque club narrowly escape relegation from the Spanish top flight.
However, after Osasuna kicked off the new campaign with defeats to Granada, Athletic Bilbao and Villarreal, Mendilibar suffered the same fate as his predecessor.
After announcing his decision at a press conference on Tuesday, chairman Miguel Archanco said: "We will find a young coach who is committed to using young players."
Osasuna, who are taking part in their 14th consecutive season in La Liga, were defeated 3-0 at home by newly promoted Villarreal on Saturday.
Should a new manager be appointed before the weekend, they will kick off their reign with a trip to face Getafe.
Mendilibar has previously managed Real Valladolid, Athletic Bilbao and Eibar.
