The dependence of the ground-state properties of weak-coupling bound magnetopolarons in quantum rods (QRs) with hydrogenic impurity on magnetic field and temperature is studied by means of the Lee-Low-Pines (LLP) transformation method and Huybrechts linear combination operator method. The expression for the ground-state energy of the magnetopolaron is derived. Results of the numerical calculations show that the ground-state energy of weak-coupling bound magnetopolarons in QRs with hydrogenic impurity increases with increasing the cyclotron frequency of the magnetic field, the confinement strength of QRs and the temperature, but decreases with increasing the electron-phonon coupling strength and the dielectric constant ratio. The stability of the ground state of magnetopolarons is closely related to the aspect ratio e′ of the QR. The ground state of magnetopolarons is the most stable at e′ =1. The stability of the ground state of magnetopolarons can remarkably decrease when the value of the aspect ratio increases or decreases from 1.