We show that the Navier-Stokes equation in O subset of R(d), d = 2, 3, around an unstable equilibrium solution is exponentially stabilizable in probability by an internal noise controller V (iota, xi) = Sigma(N)(i=1) V(i)(iota)psi(i)(xi)(beta) over dot(i)(iota), xi is an element of O, where {beta(i)}(i=1)(N) are independent Brownian motions and {psi(i)}(i=1)(N) is a system of functions on O with support in an arbitrary open subset O(0) subset of O. The stochastic control input {V(i)}(i=1)(N) is found in feedback form. The corresponding result for the linearized Navier-Stokes equation was established in [E. Barbu, The internal stabilization by noise of the linearized Navier-Stokes equation, ESAIM Control Optim. Calc. Var., to appear].