  Let $\ell$ be a prime divisor of the order of a finite unitary reflection
group. We classify up to conjugacy the parabolic and reflection subgroups that
are minimal with respect to inclusion, subject to containing an $\ell$-Sylow
subgroup. The classification assists in describing the $\ell$-Sylow subgroups
of unitary reflection groups up to group isomorphism. This classification also
relates to the modular representation theory of finite groups of Lie type. We
observe that unless a parabolic subgroup minimally containing an $\ell$-Sylow
subgroup is $G$ itself, the reflection subgroup within the parabolic minimally
containing an $\ell$-Sylow subgroup is the whole parabolic subgroup.
