Electrodynamic characteristics of a strip loop antenna located on the surface of a gyromagnetic cylinder are studied using the integral equation method. The cylinder is aligned with the gyrotropy axis and surrounded by an isotropic magnetodielectric medium. A rigorous solution for the antenna current excited by a time-harmonic given voltage is obtained. Closed-form expressions for the current distribution and input impedance of the antenna are derived in the case of a sufficiently narrow strip.