The positively charged cage framework of the natural mineral mayenite, which enables various species with negative charge to be stabilized, is one of the key structures to provide the new functionalities exploited in applications. Here we report the structural and magnetic properties of recently found eltyubyuite, Ca12Fe10Si4O32Cl6, which is the first compound bearing a transition metal oxide as a main constituent in the mayenite-type structure. From neutron powder diffraction measurements at T = 20 K and the low temperature Mossbauer measurement, we determined the magnetic structure of eltyubyuite to be a ferrirnagnet with oppositely aligned magnetic moments of +3.17(3) and -3.05(8) mu(B) in two tetrahedral Fe sites with different oxygen ligands, all bridging oxygens or mixed bridging and nonbridgirig oxygens. As far as is known, this result is likely to be a first example showing ferrimagnetism stemming from only tetrahedral Fe3+ ions. The reduced magnetic moment per Fe3+ and the resultant small net moment per unit cell of 22 mu B at mu H-0 = 5 T and T = 15 K are attributed to strong covalency in much shorter Fe-O bonds in the FeO4 tetrahedra.