In Phys. Lett. B 753, 629-638 (2016) [arXiv:1507.08188] the BESIII collaboration published a cross section measurement of the process $e^+e^-to pi^+ pi^-$ in the energy range between 600 and 900 MeV. In this erratum we report a corrected evaluation of the statistical errors in terms of a fully propagated covariance matrix. The correction also yields a reduced statistical uncertainty for the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, which now reads as $a_mu^{pipimathrm{, LO}}(600 - 900,mathrm{MeV}) = (368.2 pm 1.5_{rm stat} pm 3.3_{rm syst})times 10^{-10}$. The central values of the cross section measurement and of $a_mu^{pipimathrm{, LO}}$, as well as the systematic uncertainties remain unchanged.