The observed upper bound on the spin-down rate of the otherwise typical soft gamma-ray repeater SGR 0418+5729 has challenged the interpretation of this source as a neutron star with ultrastrong magnetic fields. Current limits imply a dipole magnetic field strength of less than 7.5 x 10(12) G, which is significantly smaller than that of a typical SGR. Independent of the properties inferred from X-ray timing, the X-ray spectra of neutron stars allow a measurement of their magnetic field strengths because they are distorted from pure blackbodies due to the presence of a magnetic field in a radiative equilibrium atmosphere. In this paper, we model high signal-to-noise ratio XMMNewton spectra of SGR 0418+5729 to place constraints on the strength of the magnetic field at the surface of the neutron star. Our analysis shows that neutron star atmosphere models with moderate magnetic field strengths (10(12-13) G) cannot fit the X-ray spectra, whereas models with stronger magnetic fields are able to account for the observations. We find that the strength of the magnetic field at the surface is 1.0 x 10(14) G. This value, although lower than all of the other SGRs analysed to date, is still high enough to generate the observed X-ray bursts from the source. In connection to the spin-down limits, it also implies a significantly non-dipolar structure of the magnetic field. We discuss the results of our spectral modelling and compare them with other SGRs.