We report on the development of a highly directional, narrow energy band, short time duration proton beam operating at high repetition rate, suitable for measurements of stopping power in high energy density plasmas as well as other applications. The protons are generated with an ultrashort-pulse laser interacting with a solid target and converted to a pencil-like narrow-band beam using a compact magnet-based energy selector. We experimentally demonstrate the production of a proton beam with an energy of 500 keV and energy spread well below 10%, and a pulse duration of 260 ps. The energy loss of this beam is measured in a 2 µm thick solid Mylar target and found to be in within 1% of theoretical predictions. The short time duration of the proton pulse makes it particularly well suited for applications involving the probing of highly transient plasma states produced in laser-matter interaction experiments, in particular measurements of proton stopping power.