A reliable, but cost-effective generation of single-photon states is key for practical quantum communication systems. For real-world deployment, waveguide sources offer optimum compatibility with fiber networks and can be embedded in hybrid integrated modules. Here, we present what we believe to be the first chip-size fully integrated fiber-coupled heralded single photon source (HSPS) module based on a hybrid integration of a nonlinear lithium niobate waveguide into a polymer board. Photon pairs at 810 nm (signal) and 1550 nm (idler) are generated via parametric down-conversion pumped at 532 nm in the LiNbO3 waveguide. The pairs are split in the polymer board and routed to separate output ports. The module has a size of (2 × 1) cm2 and is fully fiber-coupled with one pump input fiber and two output fibers. We measure a heralded second-order correlation function of g h(2)=0.05 with a heralding efficiency of η h=3.5% at low pump powers.