A measurement of the inelastic proton-proton cross section with the CMS detector at a center-of-mass energy of s√=13 TeV is presented. The analysis is based on events with energy deposits in the forward calorimeters, which cover pseudorapidities of −6.6 < η < −3.0 and +3.0 < η < +5.2. An inelastic cross section of 68.6 ± 0.5(syst) ± 1.6(lumi) mb is obtained for events with MX > 4.1 GeV and/or MY > 13 GeV, where MX and MY are the masses of the diffractive dissociation systems at negative and positive pseudorapidities, respectively. The results are compared with those from other experiments as well as to predictions from high-energy hadron-hadron interaction models.