  We study the corrections to the Casimir effect in the classical geometry of
two parallel metallic plates, separated by a distance $a$, due to the presence
of a minimal length ($\hbar\sqrt{(\beta)}$) arising from quantum mechanical
models based on a Generalized Uncertainty Principle (GUP). The approach for the
quantization of the electromagnetic field is based on projecting onto the
maximally localized states of a few specific GUP models and was previously
developed to study the Casimir-Polder effect. For each model we compute the
lowest order correction in the minimal length to the Casimir energy and find
that it scales with the fifth power of the distance between the plates $a^{-5}$
as opposed to the well known QED result which scales as $a^{-3}$ and, contrary
to previous claims, we find that it is always attractive. The various GUP
models can be in principle differentiated by the strength of the correction to
the Casimir energy as every model is characterized by a specific multiplicative
numerical constant.
