Inclusive transverse momentum spectra of eta mesons have been measured within p(T)=2-10 GeV/c at midrapidity by the PHENIX experiment in Au+Au collisions at root s(NN) = 200 GeV. In central Au+Au the eta yields are significantly suppressed compared to peripheral Au+Au, d+Au, and p+p yields scaled by the corresponding number of nucleon-nucleon collisions. The magnitude, centrality, and p(T) dependence of the suppression is common, within errors, for eta and pi(0). The ratio of eta to pi(0) spectra at high p(T) amounts to 0.40 < R-eta/pi(0)< 0.48 for the three systems, in agreement with the world average measured in hadronic and nuclear reactions and, at large scaled momentum, in e(+)e(-) collisions.