In statistical physics, the Gibbs canonical distribution is derived from the microcanonical distribution. In this article, the canonical distribution for pairwise collisions of polyatomic molecules in gases is derived from the microcanonical distribution for molecular collisions. The derivation of the canonical distribution takes into account both chaotic and regular transient state dynamics in molecular collisions by separating the vibrational-rotational states of molecules into active and passive at the moment of collision. The canonical distribution has been obtained in quadratures for the collisional activation of polyatomic molecules in equilibrium and non-equilibrium molecular media. In the classical approximation for the density of vibrational-rotational states, analytical expressions are obtained for all moments n of the canonical distribution in the form of some polynomials of the n-th order for both of these cases of collisional activation. The numbers of active degrees of freedom are estimated from a comparison of theory with experimental data on monomolecular reactions at low pressures.