We propose a mesoscopic kinetic-inductance radiation detector based on a long superconductor-normal metal-superconductor Josephson junction. The operation of this proximity Josephson sensor relies on large kinetic inductance variations under irradiation due to the exponential temperature dependence of the critical current. Coupled with a dc superconducting quantum interference device readout, the PJS is able to provide a signal to noise (S/N) ratio up to similar to 10(3) in the terahertz regime if operated as calorimeter, while electrical noise equivalent power as low as similar to 7x10(-20) W/root Hz at 200 mK can be achieved in the bolometer operation. The high performance together with the ease of fabrication make this structure attractive as an ultrasensitive cryogenic detector of terahertz electromagnetic radiation. (C) 2008 American Institute of Physics