The effect of the screening effect of the electron–phonon interaction on a weakly coupling Frohlich polaron mass has been investigated in a semiconductor hollow nanocylinder (HNC). General analytical expressions for the polaron mass have been obtained in arbitrary values of nanocylinder radius r0, taking into account screening as well as considering transitions between the subbands of dimensional quantization. The dependence of the polaron mass for the ground and excited states on nanocylinder radius has been represented on the basis of our numerical calculations. According to research carried out, it has been established that the screening contribution to polaron mass taking into account the virtual transitions from the ground state to subbands n = ±1, ±2, ±3, as well as the transitions from the polaron excited state with n = 1 to subbands n = −1, ±2,±3, is significant for a=r0/rp <1 values, where rp is the polaron radius. For values of the parameter a > 1 the screening contribution to polaron mass decreases with increasing ro, but the decrease of the polaron correction to the mass due to screening is still more than 30 %.