Pinning of superfluid vortices to the nuclear lattice of the inner crust of a neutron star supports a velocity difference between the superfluid and the solid as the star spins down. Under the Magnus force that arises on the vortex lattice, vortices undergo vortex creep through thermal activation or quantum tunnelling. We examine the hydrodynamic stability of this situation. Vortex creep introduces two low-frequency modes, one of which is unstable above a critical wavenumber for any non-zero flow velocity of the superfluid with respect to the solid. For typical pinning parameters of the inner crust, the superfluid flow is unstable over length scales ≲10 m and over time-scales as fast as months. The vortex lattice could degenerate into a tangle, and the superfluid flow could become turbulent. Unexpectedly large dissipation would suppress this instability.