The world governing body's Emergency Committee found that the election Lekjaa, who looked set to replace Ali Fassi Fihri, had not complied with FIFA rules.
FIFA explained in a statement that the FRMF "had not fulfilled its duty to comply with FIFA directives".
While Morocco's hosting of the Club World Cup in December will not be affected, FIFA has called for the FRMF to amend their election procedures before carrying out a fresh vote.
FIFA also stated that the outgoing executive will be put in charge of the federation for the time being.
"FIFA has asked the FRMF to adopt statutes in conformity with the FIFA Standard Statutes before organising new elections in the first half of 2014," the statement added.
"In the meantime, the outgoing Executive Committee will be in charge of managing the FRMF.
"The aforementioned decision will not have any effect on the organisation of the FIFA Club World Cup that is due to take place in Morocco from 11 to 21 December 2013."
Raja Casablanca and Auckland City will get the competition under way in Agadir on December 11.
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