The state Y(2175) is observed in the process e+e-→ηY(2175) with a statistical significance larger than 10 standard deviations using the data collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energies between 3.7 and 4.6 GeV. This is the first observation of the Y(2175) in this process. The mass and width of the Y(2175) are determined to be (2135±8±9) MeV/c2 and (104±24±12) MeV, respectively, and the production cross section (σ) of e+e-→ηY(2175)→ηφf0(980)→ηφπ+π- is at the several hundred femtobarn level. No significant signal for the process e+e-→η′Y(2175) is observed and the upper limit on σ(e+e-→η′Y(2175))/σ(e+e-→ηY(2175)) is estimated to be 0.43 at the 90% confidence level. We also search for ψ(3686)→ηY(2175). No significant signal is observed, indicating a strong suppression relative to the corresponding J/ψ decay, in violation of the "12% rule".