[en] In this work we report the results of calculation for quantum-mechanical rotational transitions in molecular hydrogen, H₂, induced by an ultracold ground-state antihydrogen atom H_1s. The calculations are accomplished using a nonreactive close-coupling quantum-mechanical approach. The H₂ molecule is treated as a rigid rotor. The total elastic-scattering cross section σ_el(ε) at energy ε, state-resolved rotational transition cross sections σ_jj^'(ε) between states j and j^', and corresponding thermal rate coefficients k_jj^'(T) are computed in the temperature range 0.004 K < or approx. T < or approx. 4 K. Satisfactory agreement with other calculations (variational) has been obtained for σ_el(ε).