  Occurrence of spacetime singularities is one of the peculiar features of
Einstein gravity, signalling limitation on probing short distances in
spacetime. This alludes to the existence of a fundamental length scale in
nature. On contrary, Heisenberg quantum uncertainty relation seems to allow for
probing arbitrarily small length scales. To reconcile these two conflicting
ideas in line with a well known framework of quantum gravity, several
modifications of Heisenberg algebra have been proposed. However, it has been
extensively argued that such a minimum length would introduce nonlocality in
theories of quantum gravity. In this Letter, we analyze a previously proposed
deformation of the Heisenberg algebra (i.e. $p \rightarrow p (1 + \lambda
p^{-1})$) for a particle confined in a box subjected to a gravitational field.
For the problem in hand, such deformation seems to yield an energy-dependent
behavior of spacetime in a way consistent with gravity's rainbow, hence
demonstrating a connection between non-locality and gravity's rainbow.
