A measurement of the $\mathrm{ t \bar{t} }$ production cross section at $\sqrt{s}=$ 13 TeV is presented using proton-proton collisions, corresponding to an integrated luminosity of 2.3 fb$^{-1}$, collected with the CMS detector at the LHC. Final states with one isolated charged lepton (electron or muon) and at least one jet are selected and categorized according to the accompanying jet multiplicity. From a likelihood fit to the invariant mass distribution of the isolated lepton and a jet identified as coming from the hadronization of a bottom quark, the cross section is measured to be $\sigma(\mathrm{ t \bar{t} })=$ 835 $\pm$ 3 (stat) $\pm$ 23 (syst) $\pm$ 23 (lumi) pb, in agreement with the standard model prediction. Using the expected dependence of the cross section on the pole mass of the top quark ($m_{\mathrm{ t }}$), the value of $m_{\mathrm{ t }}$ is found to be 172.7$^{+2.4}_{-2.7}$ GeV.