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The behavior of magnetic materials can be simulated at the macroscale using the micromagnetic model whose key parameters, such as exchange stiffness constants and magnetic anisotropies, can be derived from first-principles electronic structure calculations. In this work we employed the Korringa-Kohn-Rostoker (KKR) Green's function method with the coherent potential approximation (CPA) to investigate the dependence of the spin-wave stiffness on the Si concentration for the three magnetic phases of FeSi, namely A2, B2, and D03. Based on the structural, magnetic, and electronic structure analysis using the KKR-CPA methodology, the changes in the spin-wave stiffness caused by the addition of Si are primarily governed by the variations in the electronic structure.