  We calculate quantum corrections to holographic entanglement entropy in the
proposed duality between $T\bar{T}$-deformed holographic 2D CFTs and gravity in
AdS$_{3}$ with a finite cutoff. We first establish the dictionary between the
two theories by mapping the flow equation of the deformed CFT to the bulk
Wheeler-DeWitt equation. The latter reduces to an ordinary differential
equation for the sphere partition function, which we solve to find the
entanglement entropy for an entangling surface consisting of two antipodal
points on a sphere. The entanglement entropy in the inverse central charge
expansion yields the expectation value of the bulk length operator plus the
entropy of length fluctuations, in accordance with the Ryu--Takayanagi formula
and its generalization due to Faulkner, Lewkowycz, and Maldacena. Special
attention is paid to the conformal mode problem and its resolution by a choice
of contour for the gravitational path integral.
