Samples with nominal compositions of $RuSr_2(Eu_{1.34-x}Tb_xCe_{0.66})Cu_2O_z$ (x = 0, 0.67) were prepared and their superconductivity and magnetic properties were compared to shed light on the effect of Tb substitution for Eu. X-ray diffraction measurements indicate that the Tb substitution resulted in a decrease in both a and c lattice parameters in consistent with ionic size difference between Eu and Tb. Contrary to the Tb-free sample, no superconducting transition behavior is observed in the Tb-sustituted sample. It is also found that the Tb substitution for Eu significantly increases the weak-ferromagnetic component of the field-cooled magnetic susceptibility as well as an increase in the magnetic ordering temperature. These results suggest that the magnetic state of the Ru sublattice is significantly affected by the Tb substitution for Eu.