Transverse momentum spectra of neutral pions in the range 1 < p(T) < 10 GeV/c have been measured at midrapidity by the PHENIX experiment at BNL RHIC in Au+Au collisions at roots(NN)=200 GeV. The pi(0) multiplicity in central reactions is significantly below the yields measured at the same roots(NN) in peripheral Au+Au and p+p reactions scaled by the number of nucleon-nucleon collisions. For the most central bin, the suppression factor is similar to 2.5 at p(T)=2 GeV/c and increases to similar to 4-5 at p(T) approximate to 4 GeV/c. At larger p(T), the suppression remains constant within errors. The deficit is already apparent in semiperipheral reactions and increases smoothly with centrality.