This paper studies the non-linear response of the term structure of interest rates to monetary policy shocks and presents a new stylized fact. We show that uncertainty about monetary policy changes the way the term structure responds to monetary policy. A policy tightening leads to a significantly smaller increase in long-term bond yields if policy uncertainty is high at the time of the shock. We also look at the decomposition of bond yields into expectations about future policy and the term premium. The weaker response of yields is driven by the fall in term premia, which fall even more if uncertainty about policy is high. These findings are robust to the measurement of monetary policy uncertainty, the definition of the monetary policy shock and to changing the model specification. Conditional on a monetary policy shock, higher uncertainty about monetary policy tends to make yields of longer maturities relatively more attractive. As a consequence, investors demand even lower term premia. This intuition is supported by \textit{long-term} monetary policy disagreement, which leads to opposite effects with term premia increasing even more after a policy shock.