Objective. Online magnetic resonance imaging (MRI) guidance could be especially beneficial for pencil beam scanned (PBS) proton therapy of tumours affected by respiratory motion. For the first time to our knowledge, we investigate the dosimetric impact of respiratory motion on MRI-guided proton therapy compared to the scenario without magnetic field. Approach. A previously developed analytical proton dose calculation algorithm accounting for perpendicular magnetic fields was extended to enable 4D dose calculations. For two geometrical phantoms and three liver and two lung patient cases, static treatment plans were optimised with and without magnetic field (0, 0.5 and 1.5 T). Furthermore, plans were optimised using gantry angle corrections (0.5 T +5° and 1.5 T +15°) to reproduce similar beam trajectories compared to the 0 T reference plans. The effect of motion was then considered using 4D dose calculations without any motion mitigation and simulating 8-times volumetric rescanning, with motion for the patient cases provided by 4DCT(MRI) data sets. Each 4D dose calculation was performed for different starting phases and the CTV dose coverage V_95% and homogeneity D_5%-D_95% were analysed. Main results. For the geometrical phantoms with rigid motion perpendicular to the beam and parallel to the magnetic field, a comparable dosimetric effect was observed independent of the magnetic field. Also for the five 4DCT(MRI) cases, the influence of motion was comparable for all magnetic field strengths with and without gantry angle correction. On average, the motion-induced decrease in CTV V_95% from the static plan was 17.0% and 18.9% for 1.5 T and 0.5 T, respectively, and 19.9% without magnetic field. Significance. For the first time, this study investigates the combined impact of magnetic fields and respiratory motion on MR-guided proton therapy. The comparable dosimetric effects irrespective of magnetic field strength indicate that the effects of motion for future MR-guided proton therapy may not be worse than for conventional PBS proton therapy.