The shape of jets produced in quasi-real photon-proton collisions at centre-of-mass energies in the range 134-277 GeV has been measured using the hadronic energy flow. The measurement was done with the ZEUS detector at HERA. Jets are identified using a cone algorithm in the η - φ plane with a cone radius of one unit. Measured jet shapes both in inclusive jet and dijet production with transverse energies EjetT > 14 GeV are presented. The jet shape broadens as the jet pseudorapidity (ηjet) increases and narrows as EjetT increases. In dijet photoproduction, the jet shapes have been measured separately for samples dominated by resolved and by direct processes. Leading-logarithm parton-shower Monte Carlo calculations of resolved and direct processes describe well the measured jet shapes except for the inclusive production of jets with high ηjet and low EjetT. The observed broadening of the jet shape as ηjet increases is consistent with the predicted increase in the fraction of final state gluon jets.