Monetary policy shocks have a large impact on aggregate stock market returns in narrow event windows around press releases by the Federal Open Market Committee. We use spatial autoregressions to decompose the overall effect of monetary policy shocks into a direct (demand) effect and an indirect (network) effect. We attribute 50%-85% of the overall effect to indirect effects. The decomposition is robust to different sample periods, event windows, and types of announcements. Direct effects are larger for industries selling most of the industry output to end-consumers compared to other industries. We find similar evidence of large indirect effects using ex-post realized cash-fundamentals. A simple model with intermediate inputs guides our empirical methodology. Our findings indicate that production networks might be an important propagation mechanism of monetary policy to the real economy.