  On the basis of the perturbation theory in the fine structure constant
$\alpha$ and the ratio of the electron to muon masses we calculate one-loop
vacuum polarization and electron vertex corrections and the nuclear structure
corrections to the hyperfine splitting of the ground state of muonic helium
atom $(\mu e ^4_2He)$. We obtain total result for the ground state hyperfine
splitting $\Delta \nu^{hfs}=4465.526$ MHz which improves the previous
calculation of Lakdawala and Mohr due to the account of new corrections. The
remaining difference between the theoretical result and experimental value of
the hyperfine splitting equal to 0.522 MHz lies in the range of theoretical
error and requires the subsequent investigation of higher order corrections.
