We have investigated the half-metallicity and magnetism for the Heusler ferromagnet $Co_2$ZrSi interfaced with semiconductor ZnTe along the (001) plane by using the full-potential linearized augmented plane wave (FLAPW) method. We considered low types of possible interfaces: ZrSi/Zn, ZrSi/Te, Co/Zn, and Co/Te, respectively. From the calculated density of states, it was found that the half-metallicity was lost at all the interfaces, however for the Co/Te system the value of minority spin density of states was close to zero at the Fermi level. These facts are due to the interface states, appeared in the minority spin gap in bulk $Co_2$ZrSi, caused by the changes of the coordination and symmetry and the hybridizations between the interface atoms. At the Co/Te interface, the magnetic moments of Co atoms are 0.68 and $0.78{mu}_B$ for the "bridge" and "antibridge" sites, respectively, which are much reduced with respect to that ($1.15{mu}_B$) of the bulk $Co_2$ZrSi. In the case of Co/Zn, Co atoms at the "bridge" and "antibridge" sites have magnetic moments of 1.16 and $0.93{mu}_B$, respectively, which are almost same or slightly decreased compared to that of the bulk $Co_2$ZrSi. On the other hand, for the ZrSi/Zn and ZrSi/Te systems, the magnetic moments of Co atoms at the sub-interface layers are in the range of $1.13{sim}1.30;{mu}_B$, which are almost same or slightly increased than that of the bulk $Co_2$ZrSi.