  We show that the introduction of a minimal length in the context of
non-commutative spacetime gives rise (after some considerations) to
higher-order theories. We then explicitly demonstrate how these
higher-derivative theories appear as a generalization of the standard
electromagnetism and general relativity by applying a consistent procedure that
modifies the original Maxwell and Einstein-Hilbert actions. In order to set a
bound on the minimal length, we compare the deviations from the inverse-square
law with the potentials obtained in the higher-order theories and discuss the
validity of the results. The introduction of a quantum bound for the minimal
length parameter $\sqrt{\beta}$ in the higher-order QED allows us to lower the
actual limits on the parameters of higher-derivative gravity by almost half of
their order of magnitude.
