27 pages.-- MSC classes: 70F25; 37J60; 70G45.A k-symplectic framework for classical field theories subject to nonholonomic constraints is presented. If the constrained problem is regular one can construct a projection operator such that the solutions of the constrained problem are obtained by projecting the solutions of the free problem. Symmetries for the nonholonomic system are introduced and we show that for every such symmetry, there exist a nonholonomic momentum equation. The proposed formalism permits to introduce in a simple way many tools of nonholonomic mechanics to nonholonomic field theories.This work has been partially supported by MEC (Spain) Grant MTM 2007-62478, project “IngenioMathematica” (i-MATH) No. CSD 2006-00032 (Consolider-Ingenio 2010) and S-0505/ESP/0158 of the CAM. Silvia Vilariño acknowledges the financial support of Xunta de Galicia Grants IN840C 2006/119-0 and IN809A 2007/151-0.Peer reviewed