A Penning-trap facility for high-precision mass spectrometry based on a novel detection method has been built. This method consists in measuring motional frequencies of singly-charged ions trapped in strong magnetic fields through the fluorescence photons from laser-cooled 40Ca+ ions, to overcome limitations faced in electronic single-ion detection techniques. The key element of this facility is an open-ring Penning trap coupled upstream to a preparation Penning trap similar to those used at Radioactive Ion Beam facilities. Here we present a full characterization of the trap and demonstrate motional frequency measurements of trapped ions stored by applying external radiofrequency fields in resonance with the ions' eigenmotions, in combination with time-of-flight identification. The infrastructure developed to observe the fluorescence photons from 40Ca+, comprising the 12 laser beams and the optical system to register the image in a high-sensitive CCD sensor, has been proved by taking images of the trapped and cooled 40Ca+ ions. This demonstrates the functionality of the proposed laser-based mass-spectrometry technique, providing a unique platform for precision experiments with implications in different fields of physics.