  The response of thin films of Bi$_2$Se$_3$ to a strong perpendicular magnetic
field is investigated by performing magnetic bandstructure calculations for a
realistic multi-band tight-binding model. Several crucial features of Landau
quantization in a realistic three-dimensional topological insulator are
revealed. The $n=0$ Landau level is absent in ultra-thin films, in agreement
with experiment. In films with a crossover thickness of five quintuple layers,
there is a signature of the $n=0$ level, whose overall trend as a function of
magnetic field matches the established low-energy effective-model result.
Importantly, we find a field-dependent splitting and a strong spin-polarization
of the $n=0$ level which can be measured experimentally at reasonable field
strengths. Our calculations show mixing between the surface and bulk Landau
levels which causes the character of levels to evolve with magnetic field.
