An ab initio calculation of the hyperfine splitting (HFS) intervals in the 2s_1/2^(mu)1s_1/2^(e) state of the exotic (⁴He²⁺ - mu^-e^-)⁰ and (³He²⁺ - mu^-e^-)⁰ atoms is carried out. The smallness of beta = m_e/m_mu approximately 1/200 (the electron and the mu-meson mass ratio) enables us to take into account the non-relativistic interparticle correlational interaction perturbatively. Corresponding corrections, which give the dominant contribution to the HFS, are calculated to logarithmic accuracy analytically and exactly. Together with the leading relativistic and radiative corrections the HFS values obtained turn out to be in accord with the results of other calculations.