Magnetism and the origin of ferroelectricity in the multiferroic MnWO₄ are studied using ab initio electronic-structure calculations, correctly reproducing the magnetic ground state. The calculated ferroelectric polarization is in good agreement with experiments. Our results reveal that spin-orbit interaction is necessary and sufficient to explain the observed ferroelectric polarization, establishing an entirely electronic origin of ferroelectricity in MnWO₄. The origin of spin-orbit interaction in this compound with a nominally d⁵ L=0 orbitally quenched state is elucidated by analyzing results of x-ray absorption spectroscopy.