It is a remarkable achievement for the tiny island nation, which is located on an archipelago off the northwest coast of the continent.
The Blue Sharks have replaced giants Ivory Coast at the summit, with the African champions dropping down to second spot.
Cameroon also improved, moving into the top 10 at the expense of Guinea.
Top 10 African sides in Fifa's rankings for March
1. Cape Verde Islands
2. Ivory Coast
3. Algeria
4. Ghana
5. Tunisia
6. Senegal
7. Egypt
8. DR Congo
9. Congo
10. Cameroon
Cape Verde have moved to the top of the list of African sides in Fifa's world rankings for March.