Soft-γ-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are slowly rotating, isolated neutron stars that sporadically undergo episodes of long-term flux enhancement (outbursts) generally accompanied by the emission of short bursts of hard X-rays. This behaviour can be understood in the magnetar model, according to which these sources are mainly powered by their own magnetic energy. This is supported by the fact that the magnetic fields inferred from several observed properties of SGRs and AXPs are greater than-or at the high end of the range of-those of radio pulsars. In the peculiar case of SGR 0418+5729, a weak dipole magnetic moment is derived from its timing parameters, whereas a strong field has been proposed to reside in the stellar interior and in multipole components on the surface. Here we show that the X-ray spectrum of SGR 0418+5729 has an absorption line, the properties of which depend strongly on the star's rotational phase. This line is interpreted as a proton cyclotron feature and its energy implies a magnetic field ranging from 2 × 10(14) gauss to more than 10(15) gauss.