A measurement of the inelastic proton-proton cross section with the CMS detector at a center-of-mass energy of root s = 13 TeV is presented. The analysis is based on events with energy deposits in the forward calorimeters, which cover pseudorapidities of -6.6 < eta < -3.0 and +3.0 < eta < +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.