A measurement of the inelastic proton-proton cross section with the CMS detector at a center-of-mass energy of $ \sqrt{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 M${X}$ > 4.1 GeV and/or M${Y}$ > 13 GeV, where M${X}$ and M${Y}$ 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.