The French side have slipped to 17th in the Ligue 1 table, one place outside the relegation zone, after a run of eight games without a win in all competitions.
Fernandez, 59, in the summer was named Montpellier boss just a year after Rene Girard had led the club to their first ever French title.
Montpellier won their only ever title in 2012, picking up 82 points – the second highest total in Ligue 1 history – to beat Paris St-Germain to the crown.
Girard fell out with club president Louis Nicollin, who refused to offer him a new contract at the end of last season.
In April, Nicollin confirmed that former Marseille, Auxerre and Nancy boss Fernandez would take over as manager on 1 July.
However, Fernandez only led them to two wins from his 16 league and one cup match in charge.
Montpellier finished ninth last season and 14th the year before their shock title success.