24 pages, 2 figures.-- Published in: JHEP09(2007)087.We study possible patterns of neutrino masses and mixings in string models in which Majorana neutrino masses are generated by a certain class of string theory instantons recently considered in the literature. These instantons may generate either directly the dim=5 Weinberg operator or right-handed neutrino Majorana masses, both with a certain flavour-factorised form. A hierarchy of neutrino masses naturally appears from the exponentially suppressed contributions of different instantons. The flavour structure is controlled by string amplitudes involving neutrino fields and charged instanton zero modes. For some simple choices for these amplitudes one finds neutrino mixing patterns consistent with experimental results. In particular, we find that a tri-bimaximal mixing pattern is obtained for simple symmetric values of the string correlators.This work has been partially supported by the European Commission under the RTN European Program MRTN-CT-2004-503369, the CICYT (Spain), and the Comunidad de Madrid under project HEPHACOS, P-ESP-00346.