The Mantel-Haenszel (MH) method has been used for decades to synthesize data obtained from studies that compare two interventions with respect to a binary outcome. It has been shown to perform better than the inverse-variance method or Peto's odds ratio when data is sparse. Network meta-analysis (NMA) is increasingly used to compare the safety of medical interventions, synthesizing, eg, data on mortality or serious adverse events. In this setting, sparse data occur often and yet there is to-date, no extension of the MH method for the case of NMA. In this paper, we fill this gap by presenting a MH-NMA method for odds ratios. Similarly to the pairwise MH method, we assume common treatment effects. We implement our approach in R, and we provide freely available easy-to-use routines. We illustrate our approach using data from two previously published networks. We compare our results to those obtained from three other approaches to NMA, namely, NMA with noncentral hypergeometric likelihood, an inverse-variance NMA, and a Bayesian NMA with a binomial likelihood. We also perform simulations to assess the performance of our method and compare it with alternative methods. We conclude that our MH-NMA method offers a reliable approach to the NMA of binary outcomes, especially in the case or sparse data, and when the assumption of methodological and clinical homogeneity is justifiable.