To the best of my knowledge, Islamic nations are members of an organization called "Organisation of Islamic Conference." The spelling is British. In Arabic it is called

منظمة المؤتمر الإسـلامي

Pronounced: MUNAZH-ZHAMAT AL-MU'TAMAR AL-ISLAMIYY

If "Federation of Islamic Nations" is a hypothetical organization, I would translate the phrase as follows:

اتحاد الأمم الإسـلامية

Pronounced: ITTIHAD AL-UMAM AL-ISLAMIYYA

Fuad

Again, if this is merely a hypothetical organization, you may want to name it Federation of Isalmic States rather than Nations. Muslims tend to speak of themselves as one nation, despite the multiplicity of polities. In Arabic that would be ITTIHAD AL-DUWAL AL-ISLAMIYYA

اتحاد الدول الإسـلامية

Fuad

This is based on my current experience in the field of immigration and refugee cases, where I would expect to hear all sort of names or combination of words. Any way, the words "Federation" and "Islamic" do exist together (i.e. in the attached reference;) and on that bases I would propose a relatively different answer to meet the source context requirement; and leave the question if such an organization/Federation do exist or not to the source.