  We show that linear perturbations around the simplest black hole solution of
massive bi-gravity theories, the bi-Schwarzschild solution, exhibit an unstable
mode featuring the Gregory-Laflamme instability of higher-dimensional black
strings. The result is obtained for the massive gravity theory which is free
from the Boulware-Deser ghost, as well as for its extension with two dynamical
metrics. These results may indicate that static black holes in massive gravity
do not exist. For graviton mass of order of Hubble scale, however, the
instability timescale is of order of the Hubble time.
