In this paper we incorporate a labor market with matching frictions and wage rigidities into the New Keynesian business cycle model. In particular, we analyze the effect of a monetary policy shock and investigate how labor market frictions affect the transmission process of monetary policy. The model allows real wage rigidities to interact with adjustments in employment and hours affecting inflation dynamics via marginal costs. We find that the response of unemployment and inflation to an interest rate innovation depends on the degree of wage rigidity. Generally, more rigid wages translate into more persistent movements of aggregate inflation. Moreover, the impact of a monetary policy shock on unemployment and inflation depends also on labor market fundamentals such as bargaining power and the flows in and out of employment.