We investigate quantum corrections to the classical four-dimensional low-energy effective action of type II string theory compactified on SU(3) structure geometries. Various methods previously developed for Calabi-Yau compactifications are adopted to constrain - under some simple assumptions about the low-energy degrees of freedom - the leading perturbative corrections to the moduli space metrics in both alpha' and the string coupling constant. We find that they can be parametrized by a moduli dependent function in the hypermultiplet sector and a constant in the vector multiplet sector. We argue that under specific additional assumption they take - in complete analogy to the Calabi-Yau case - a universal form which depends only on the Euler characteristic of the six-dimensional compact space.