We have conceived, built, and operated a device for the non-destructive single-pass detection of charged particles in a beamline. The detector is based on the non-resonant pick-up and subsequent low-noise amplification of the image charges induced in a cylindrical electrode surrounding the particles' beam path. The first stage of the amplification electronics is designed to be operated from room temperature down to liquid helium temperature. The device represents a non-destructive charge counter as well as a sensitive timing circuit. We present the concept and design details of the device. We have characterized its performance and show measurements with low-energy highly charged ions (such as Ar(13+)) passing through one of the electrodes of a cylindrical Penning trap. This work demonstrates a novel approach of non-destructive, low noise detection of charged particles which is, depending on the bunch structure, suitable, e.g., for ion traps, low-energy beamlines or accelerator transfer sections.