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By using broadband dielectric spectroscopy in the radio frequency and microwave range, we studied the magnetoelectric dynamics in the multiferroic chiral antiferromagnet MnWO_{4}. Above the multiferroic phase transition at T_{N2}≈12.6  K we observe a critical slowing of the corresponding magnetoelectric fluctuations resembling the soft-mode behavior in canonical ferroelectrics. This electric-field-driven excitation carries much less spectral weight than ordinary phonon modes. Also, the critical slowing down of this mode scales with an exponent larger than 1, which is expected for magnetic second-order phase transition scenarios. Therefore, the investigated dynamics have to be interpreted as the softening of an electrically active magnetic excitation, an electromagnon.