The 42-year-old -- who inspired France to the 1998 World Cup trophy and was also a member of the Euro 2000 title winning side -- has been coaching Real's reserve side Castilla but the federation claims he does not possess the required coaching qualifications.
Real have said they will appeal against the punishment by 'all legal avenues open to them'.
The reserve team's assistant coach Santiago Sanchez was also punished.
They pointed out that Zidane "has been authorised by the French Football Federation to work as a head coach in the category Real Madrid Castilla currently find themselves in".
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Zidane -- who was linked with the head coach post at another of his former clubs Bordeaux in the close season -- was elevated to reserve team coach at the beginning of this season following a single campaign as Carlo Ancelotti's assistant which saw Real win a 10th European Cup in May.
The case has sparked controversy in Spain with national team coach Vicente del Bosque telling Cope radio station that "everyone should have a coaching badge".
Rayo Vallecano coach Paco Jemez used tougher language, describing Real's actions as "shameful".
However, both Ancelotti and Dutch football legend Johan Cruyff have spoken out in support of Zidane.