Low-mass X-ray binaries (LMXBs) that show thermonuclear bursts are ideal sources for constraining the equation of state of neutron star matter. The lack of independent distance measurements for most of these sources, however, prevent a systematic exploration of the masses and radii of the neutron stars, hence limiting the equation-of-state studies. We present here a measurement of the distance to the LMXB 4U 1608-52 that is based on the study of the interstellar extinction toward the source. We first model the individual absorption edges of the elements Ne and Mg in the high-resolution X-ray spectrum obtained with XMM-Newton. We then combine this information with a measurement of the run of reddening with distance using red clump stars and determine a minimum distance to the source of 3.9 kpc, with a most probable value of 5.8 kpc. Finally, we analyze time-resolved X-ray spectra of Type I X-ray bursts observed from this source to measure the mass and the radius of the neutron star. We find a mass of M = 1.74 ± 0.14 M sun and a radius of R = 9.3 ± 1.0 km, respectively. This mass and radius can be achieved by several multi-nucleon equations of state.