Inclusive jet production in pPb collisions at a nucleon–nucleon (NN) center-of-mass energy of $\sqrt{s_{_\mathrm {NN}}} =5.02,\mathrm{TeV} $ is studied with the CMS detector at the LHC. A data sample corresponding to an integrated luminosity of 30.1 nb$^{-1}$ is analyzed. The jet transverse momentum spectra are studied in seven pseudorapidity intervals covering the range $ -2.0<\eta _\mathrm {CM}< 1.5$ in the NN center-of-mass frame. The jet production yields at forward and backward pseudorapidity are compared and no significant asymmetry about $\eta _\mathrm {CM} = 0$ is observed in the measured kinematic range. The measurements in the pPb system are compared to reference jet spectra obtained by extrapolation from previous measurements in pp collisions at $\sqrt{s}=7,\mathrm{TeV} $ . In all pseudorapidity ranges, nuclear modifications in inclusive jet production are found to be small, as predicted by next-to-leading order perturbative QCD calculations that incorporate nuclear effects in the parton distribution functions.