Invariant yields of neutral pions at midrapidity in the transverse momentum range \(0.6 <{p_\mathrm{T}} <12\,{\mathrm {GeV}}/\)c measured in Pb–Pb collisions at \({\sqrt{s_\mathrm{{NN}}}} =2.76\) TeV are presented for six centrality classes. The pp reference spectrum was measured in the range \(0.4 <{p_\mathrm{T}} <10\,{\mathrm {GeV}}/\)c at the same center-of-mass energy. The nuclear modification factor, \(R_\mathrm{{AA}}\), shows a suppression of neutral pions in central Pb–Pb collisions by a factor of up to about \(8{-}10\) for \(5 \lesssim {p_\mathrm{T}} \lesssim 7\,{\mathrm {GeV}}/\)c. The presented measurements are compared with results at lower center-of-mass energies and with theoretical calculations.