Abstract We present a theory of phonon-drag thermopower, S x x g , in MoS₂ monolayer at a low-temperature regime in the presence of a quantizing magnetic field B. Our calculations for S x x g consider the electron–acoustic phonon interaction via deformation potential (DP) and piezoelectric (PE) couplings for longitudinal (LA) and transverse (TA) phonon modes. The unscreened TA-DP is found to dominate S x x g over other mechanisms. The S x x g is found to oscillate with the magnetic field where the lifting effect of the valley and spin degeneracies in MoS₂ monolayer has been clearly observed. An enhanced S x x g with a peak value of ∼ 1 mV K⁻¹ at about T = 10 K is predicted, which is closer to the zero field experimental observation. In the Bloch–Grüneisen regime the temperature dependence of S x x g gives the power-law S x x g ∝ T δ e , where δ _e varies marginally around 3 and 5 for unscreened and screened couplings, respectively. In addition, S x x g is smaller for larger electron density n _e . The power factor PF is found to increase with temperature T, decrease with n _e , and oscillate with B. The prediction of an increase of thermal conductivity with temperature and the magnetic field is responsible for the limit of the figure of merit (ZT). At a particular magnetic field and temperature, ZT can be maximized by optimizing electron density. By fixing n e = 10 12 cm⁻², the highest ZT is found to be 0.57 at T = 5.8 K and B = 12.1 T. Our findings are compared with those in graphene and MoS₂ for the zero-magnetic field.