  The de Haas-van Alphen (dHvA) signal arising from orbits on the $\pi$ Fermi
surface sheet of the two-gap superconductor MgB$_2$ has been observed in the
vortex state below $H_{c2}$. An extra attenuation of the dHvA signal, beyond
those effects described in the conventional Lifshitz-Kosevich expression, is
seen due to the opening of the superconducting gap. Our data show that the
$\pi$ band gap is still present up to $H_{c2}$. The data are compared to
current theories of dHvA oscillations in the superconducting state which allow
us to extract estimates for the evolution of the $\pi$ band gap with magnetic
field. Contrary to results for other materials, we find that the most recent
theories dramatically underestimate the damping in MgB$_2$.
