  In the present work, we investigate the consequences of running gravitational
coupling on the properties of the three-dimensional BTZ black hole. We take as
starting point the functional form of gravitational coupling obtained in the
context of asymptotic safe gravity theory. By using the standard scale setting
relation where $k\sim \xi/r^n$, we compute the solution of the Einstein field
equations. We get and analyze the horizon and the thermodynamic properties of
this new class of black hole solutions. The impact of the scale--dependent
parameter $\xi$ on the cosmological "constant" and metric functions are briefly
discussed. We find that the null energy condition is also violated in this
setup when scale-dependent gravity and Newton's coupling (coming from the
asymptotic safety scenario of gravity) are simultaneously taken into account.
