We calculate the cross section of inclusive direct J/psi photoproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics for the first time including the full relativistic corrections due to the intermediate S-1(0){[}8], S-3(1){[}8], and 3P(J)({[}8]) color-octet states. A comparison of our results to recent H1 data suggests that the color-octet mechanism is indeed realized in J/psi photoproduction, although the predictivity of our results still suffers from uncertainties in the color-octet long-distance matrix elements.