I find that shadow bank money creation significantly expands during monetary tightening. This "shadow money channel" offsets the reductions in commercial bank deposits and dampens the impact of monetary policy. Using a structural model of bank competition, I show that heterogeneous depositor clientele quantitatively explains the difference in monetary transmission between commercial and shadow banks. Facing more yield-sensitive clientele, shadow banks pass through more rate hikes to depositors, thereby attract more deposits when the Fed raises rates. My results suggest that monetary tightening may unintentionally drive deposits into the uninsured shadow banking sector, amplifying the risk of bank runs.