Signal modulation in optoelectronics is obtained by modulation of either the refractive index or the absorbance by an electric field. However, electromodulators have not kept up with the miniaturization of other electronic and optical components. Here we show a strong transverse electroabsorption signal in a monolayer of the 2D semiconductor MoS2. The electroabsorption spectrum is dominated by an apparent linewidth broadening of around 15% at a modulated voltage of only V-pp = 0.5 V. Contrary to known variants of the Stark effect, the broadening increases linearly with the applied field strength and arises from a linear variation of the distance between the strongly overlapping exciton and trion resonances. The achievable modulation depths exceeding 0.1 dB nm(-1) bear the scope for extremely compact, ultrafast, energy-efficient electroabsorption modulators for integrated photonics, including on-chip optical communication.