One shows that the linearized Navier-Stokes equation in ${\mathcal{O}}{\subset} R^d,\;d \ge 2$, around an unstable equilibrium solution is exponentially stabilizable in probability by an internal noise controller $V(t,\xi)=\displaystyle\sum\limits_{i=1}^{N} V_i(t)\psi_i(\xi) \dot\beta_i(t)$, $\xi\in{\mathcal{O}}$, where $\{\beta_i\}^N_{i=1}$ are independent Brownian motions in a probability space and $\{\psi_i\}^N_{i=1}$ is a system of functions on ${\mathcal{O}}$ with support in an arbitrary open subset ${\mathcal{O}}_0\subset {\mathcal{O}}$. The stochastic control input $\{V_i\}^N_{i=1}$ is found in feedback form. One constructs also a tangential boundary noise controller which exponentially stabilizes in probability the equilibrium solution.