The stability and magnetic properties of Fe clusters in the (Ga,Fe)N magnetic semiconductor is investigated by using first-principles density functional theory and local spin density+Hubbard U theoretical methods. The present results reveal the existence of ferrimagnetic clusters formed by three or four peripheral Fe atoms neighboring a central Fe atom acting as a robust magnetic anchoring point. These clusters have magnetic moments 2 or 3 times that of a single Fe atom and, when connected by sharing peripheral Fe atoms, can form stable, ordered magnetic regions where all of the central atoms are ferromagnetically coupled. The formation of these ferrimagnetic clusters is proposed here to be at the origin of the ferromagnetic behavior observed in (Ga,Fe)N samples showing chemical phase separation.