  We introduce a UV cutoff into free scalar field theory on the noncommutative
(fuzzy) two-sphere. Due to the IR-UV connection, varying the UV cutoff allows
us to control the effective nonlocality scale of the theory. In the resulting
fuzzy geometry, we establish which degrees of freedom lie within a specific
geometric subregion and compute the associated vacuum entanglement entropy.
Entanglement entropy for regions smaller than the effective nonlocality scale
is extensive, while entanglement entropy for regions larger than the effective
nonlocality scale follows the area law. This reproduces features previously
obtained in the strong coupling regime through holography. We also show that
mutual information is unaffected by the UV cutoff.
