  We investigate the structure of the gravity-induced Generalized Uncertainty
Principle in three dimensions. The subtleties of lower dimensional gravity, and
its important differences with respect to four and higher dimensions, are duly
taken into account, by considering different possible candidates for the
gravitational radius, $R_g$, that is the minimal length/maximal resolution of
the quantum mechanical localization process. We find that the event horizon of
the $M \neq 0$ Ba\~{n}ados-Teitelboim-Zanelli micro black hole furnishes the
most consistent $R_g$. This allows us to obtain a suitable formula for the
Generalized Uncertainty Principle in three dimensions, and also to estimate the
corrections induced by the latter on the Hawking temperature and Bekenstein
entropy. We also point to the extremal $M=0$ case, and its natural unit of
length introduced by the cosmological constant, $\ell = 1 / \sqrt{-\Lambda}$,
as a possible alternative to $R_g$, and present a condensed matter analog
realization of this scenario.
