Let's look at the map. What countries are involved?

70% or more prevalence:
Egypt - 90%-94.7% Muslim
Sudan - 97% Muslim
Ethiopia - 33.9% Muslim
Eritrea - 36-51.6% Muslim
Somalia - 99.8% Muslim
Djibouti - 97% Muslim
Mali - 95% Muslim
Guinea - 89.1% Muslim
Sierra Leone - 78.6% Muslim
Gambia - 95.7% Muslim
Burkina Faso - 61.5% Muslim

50% or more prevalence:
Liberia - 20% Muslim
Mauritania - 100% Muslim

30% or more prevalence:
Cote d'Ivoire 42.9% Muslim
Guinea-Bissau - 45.1% Muslim
Chad - 58% Muslim

10% or more prevalence:
Yemen - 99.1% Muslim
Nigeria - 47.6-51.6% Muslim
Senegal - 96.1% Muslim
Central African Republic
Kenya - 11.2% Muslim
Tanzania - 35.2% Muslim

Less than 10% prevalence:
Iraq -95.7% Muslim
Ghana - 18% Muslim
Togo - 20% Muslim
Benin 27.7% Muslim
Niger - 98.3% Muslim
Cameroon - 30% Muslim
Uganda - 14% Muslim

Suspiciously Absent:
Saudi Arabia
South Sudan

Yes, the overlap is not 1 to 1. Ethiopia and Egypt have numbers that are impossible if we don't concede that some non-Muslims engage in the practice. HOWEVER, generally the higher the percentage of Muslims in an African country, the greater the likelihood that female genital mutilation occurs in higher percentages. Also, I would point out that the only Sub-Saharan countries with more than 10% of the population being Muslim that don't occur on the chart are Malawi and South Sudan. The latter is probably due to a lack of accurate reporting.

The practice did have roots in local traditions, certainly. However, it's been kept alive and perpetuated almost solely within the context of Islam, with only minor exception (Egyptian and Ethiopian Christians, Liberia for some odd reason).