Dijet production has been measured in pPb collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV. A data sample corresponding to an integrated luminosity of 35 inverse-nanobarns was collected using the Compact Muon Solenoid detector at the Large Hadron Collider. The dijet transverse momentum balance, azimuthal angle correlations, and pseudorapidity distributions are studied as a function of the transverse energy in the forward calorimeters ($E_T^{4\lt |\eta| \lt 5.2}$). For pPb collisions, the dijet transverse momentum ratio and the width of the distribution of dijet azimuthal angle difference are comparable to the same quantities obtained from a simulated pp reference and insensitive to $E_T^{4\lt |\eta| \lt 5.2}$. In contrast, the mean value of the dijet pseudorapidity is found to change monotonically with increasing $E_T^{4\lt |\eta| \lt 5.2}$, indicating a correlation between the energy emitted at large pseudorapidity and the longitudinal motion of the dijet frame. The pseudorapidity distribution of the dijet system is compared with next-to-leading-order perturbative QCD predictions obtained from both nucleon and nuclear parton distribution functions, and the data more closely match the latter.