This paper shows how interbank market fragmentation disrupts monetary policy implementation. Fragmentation is defined as the situation where some banks are cut from the interbank loan market. The paper incorporates fragmentation in an otherwise standard theoretical model of monetary policy implementation, where profit maximizing banks, subject to reserve requirements, borrow and deposit funds at a central bank. It shows that in the presence of fragmentation, excess liquidity arises endogenously and the interbank rate declines below the central bank main rate. The interbank rate is then unstable. The paper documents that this is what happened in the Euro-Area since 2008. The model is also well suited to analyze unconventional monetary policy measures.