We present results of experimental studies of the effect of weak magnetic field (H = 300 Oe) on the intensity of terahertz radiation (λ = 100 µm) of hot electrons from n-Ge at the near liquid helium temperatures (T ≈ 5 K) when both electric and magnetic fields are oriented along the same direction. Strong effect of the weak magnetic field (reduction of the radiation intensity by a factor of 3–10) is observed to occur under relatively weak electric fields (5–15 V/cm), thus demonstrating a switch-like effect. We show experimentally that this strong effect is due to sharp decrease of the free carrier concentration by means of suppression of the donor ionization by the magnetic field. Much less reduction of the radiation intensity (up to 20% of the initial value) caused by the weak magnetic field is reliably detected under stronger electric fields (100–200 V/cm) when all donors are ionized and the influence of the magnetic field on the carrier concentration is expected to be absent. We propose a theoretical model to explain the subtle effect of the weak magnetic field on the THz hot electron radiation at stronger electric fields which reveals through the longitudinal magnetoresistance. The longitudinal magnetoesistance is shown to become essential due to anisotropy of the electron energy dispersion law and due to strong modification of the electron velocity distribution function by stronger electric fields. Our theoretical estimations well agree with our experimental results.