  In this paper, we study the Casimir effect in the classical geometry of two
parallel conducting plates, separated by a distance $L$, due to the presence of
a minimal length $\lambda$ arising from a background independent (polymer)
quantization scheme. To this end, we polymer-quantize the classical
Klein-Gordon Hamiltonian for a massive scalar field confined between the plates
and obtain the energy spectrum. The minimal length scale of the theory
introduces a natural cutoff for the momenta in the plane parallel to the plates
and a maximum number of discrete modes between the plates. The zero-point
energy is calculated by summing over the modes, and by assuming $\lambda \ll
L$, we expressed it as an expansion in powers of $1/N$, being $N=L/ \lambda$
the number of points between the plates. Closed analytical expressions are
obtained for the Casimir energy in the cases of small and large scalar mass
limits.
