Accumulating electrons in transparent conductive oxides such as indium tin oxide (ITO) can induce an "epsilon-near-zero" (ENZ) in the spectral region near the important telecommunications wavelength of λ = 1.55 μm. Here we theoretically demonstrate highly effective optical electro-absorptive modulation in a silicon waveguide overcoated with ITO. This modulator leverages the combination of a local electric field enhancement and increased absorption in the ITO when this material is locally brought into an ENZ state via electrical gating. This leads to large changes in modal absorption upon gating. We find that a 3 dB modulation depth can be achieved in a non-resonant structure with a length under 30 μm for the fundamental waveguide modes of either linear polarization, with absorption contrast values as high as 37. We also show a potential for 100 fJ/bit modulation, with a sacrifice in performance.