We present optical and ultraviolet observations of nearby Type Ic supernova (SN Ic) SN 2017ein, as well as a detailed analysis of its progenitor properties from both the early-time observations and the prediscovery Hubble Space Telescope (HST) images. The optical light curves started from within 1 day to similar to 275 days after explosion, and optical spectra range from similar to 2 days to similar to 90 days after explosion. Compared to other normal SNe Ic like SN 2007gr and SN 2013ge, SN 2017ein seems to have more prominent C II absorption and higher expansion velocities in early phases, suggestive of relatively lower ejecta mass. The earliest photometry obtained for SN 2017ein shows indications of shock cooling. The best fit obtained by including a shock-cooling component gives an estimate of the envelope mass as similar to 0.02 M-circle dot and stellar radius as 8 +/- 4 R-circle dot. Examining the pre-explosion images taken with the HST WFPC2, we find that the SN position coincides with a luminous and blue point-like source, with an extinction-corrected absolute magnitude of M-V similar to -8.2 mag and M-I similar to -7.7 mag. Comparisons of the observations to the theoretical models indicate that the counterpart source was either a single W-R star or a binary whose members had high initial masses, or a young compact star cluster. To further distinguish between different scenarios requires revisiting the site of the progenitor with HST after the SN fades away.