  An equation for the quantum average of the gauge invariant Wilson loop in
non-commutative Yang-Mills theory with gauge group U(N) is obtained. In the 't
Hooft limit, the equation reduces to the loop equation of ordinary Yang-Mills
theory. At finite $N$, the equation involves the quantum averages of the
additional gauge invariant observables of the non-commutative theory associated
with open contours in space-time. We also derive equations for correlators of
several gauge invariant (open or closed) Wilson lines. Finally, we discuss a
perturbative check of our results.
