Fano resonance is a fundamental physical process that strongly affects the electronic transport, optical, and vibronic properties of matter. Here, we provide the first experimental demonstration of its profound effect on spin properties in semiconductor nanostructures. We show that electron spin generation in InAs/GaAs quantum-dot structures is completely quenched upon spin injection from adjacent InGaAs wetting layers at the Fano resonance due to coupling of light-hole excitons and the heavy-hole continuum of the interband optical transitions, mediated by an anisotropic exchange interaction. Using a master equation approach, we show that such quenching of spin generation is robust and independent of Fano parameters. This work therefore identifies spin-dependent Fano resonance as a universal spin loss channel in quantum-dot systems with an inherent symmetry-breaking effect.