The dynamic behavior of microtubules in solution can be strongly modified by interactions with walls or other structures. We examine here a microtubule growth model where the increase in size of the plus-end is perturbed by collisions with other microtubules. We show that such a simple mechanism of constrained growth can induce ordered structures and patterns from an initially isotropic and homogeneous suspension. We find that microtubules self-organize locally in randomly oriented domains that grow and compete with each other. A weak orientation bias, similar to the one induced by gravity or cellular boundaries is enough to influence the domain growth direction, eventually leading to a macroscopic sample orientation.