Core-shell GaN nanowires are expected to be building blocks of future light emitting devices. Here we apply off-axis electron holography to map the electrostatic potential distributions in such nanowires. To access the cross-section of selected individual nanowires, focused ion beam (FIB) milling is used. Furthermore, to assess the influence of FIB damage, the dopant potential measured from an intact NW is compared with a FIB prepared one. It is shown that in addition to the built-in potential between the p-type shell and unintentionally n-type under-layer there is a potential barrier between the core and under-layer which are both unintentionally n-type doped.