We have measured susceptibility, specific heat, resistivity, and thermopower of CaCu$_3$Ti$_{4-x}$Ru$_x$O$_{12}$ and CaCu$_{3-y}$Mn$_y$Ru$_4$O$_{12}$, and have found that CaCu$_3$Ru$_4$O$_{12}$ can be regarded as a heavy-fermion oxide in d-electron systems. The Kondo temperature is near 200 K, and the susceptibility (1.4$times10^{-3}$ emu/Cu mol) and the electron specific heat coefficient (28 mJ/Cu molK$^2$) are moderately enhanced. The resistivity is proportional to $T^2$ at low temperatures, and satisfies the Kadowaki-Woods relation. The heavy-fermion state comes from the interaction between the localized moment of Cu 3d and the conduction electron of Ru 4d. An insulator-metal transition occurs between $x=1.5$ and 4 in CaCu$_3$Ti$_{4-x}$Ru$_x$O$_{12}$, which can be regarded as a transition from magnetic insulator to heavy-fermion metal.