Nuclear magnetic resonance and magnetization measurements were used to probe the magnetic features of single-crystalline Bi(Cu(1-x)Zn(x))(2)PO(6) with 0<x<0.05 at temperatures between 2.6 K and 300 K. The simple line shape of the (31)P NMR signals of the pristine compound changes considerably for x>0 and we present clear evidence for a temperature-dependent variation of the local magnetization close to the Zn sites. The generic nature of this observation is indicated by results of model calculations on appropriate spin systems of limited size employing quantum Monte Carlo methods.