We present the first measurements of the Fe K alpha line profile in NGC 4151 from ASCA observations performed in 1993 May, November, and December. The apparent line profile is asymmetric, consisting of a peak at ~6.3--6.4 keV, a sharp drop on the blue side below ~7 keV, and a broad red wing extending to ~4--5 keV. This first clear indication of complex structure confirms earlier tentative measurements of the Fe-K region with the Broad Band X-Ray Telescope (BBXRT). The line intensity, equivalent width, and detailed shape are model dependent. Interpretation of the profile in terms of emission from a disk rotating around a central black hole strongly constrains the putative disk to be face on, but this contradicts the current body of knowledge of the geometry of this source. If the apparent red wing is not in fact part of a peculiar continuum, then a face-on disk may be allowed only if the collimated structure observed at the parsec scale is misaligned with respect to the disk normal by at least 20 deg and iron is overabundant by a factor of ~2, with some additional caveats. Alternatively, a different geometry of line-emitting material may be required. In contrast to clear variability in the soft X-ray line emission below ~1 keV between the observations, these data show no significant variability of the Fe K alpha overall line shape, intensity, or equivalent width.