  The non zero value of Planck constant $h$ underlies the emergence of several
inequalities that must be satisfied in the quantum realm, the most prominent
one being Heisenberg Uncertainty Principle. Among these inequalities,
Bekenstein bound provides a universal limit on the entropy that can be
contained in a localized quantum system of given size and total energy. In this
Letter, we explore how Bekenstein bound is affected when Heisenberg uncertainty
relation is deformed so as to accommodate gravitational effects close to Planck
scale (Generalized Uncertainty Principle). By resorting to general
thermodynamic arguments, and in regimes where the equipartition theorem still
holds, we derive in this way a "generalized Bekenstein bound". Physical
implications of this result are discussed for both cases of positive and
negative values of the deformation parameter.
