Context. Low-mass stars in eclipsing binary systems show radii larger and effective temperatures lower than theoretical stellar models predict for isolated stars with the same masses. Eclipsing binaries with low-mass components are hard to find due to their low luminosity. As a consequence, the analysis of the known low-mass eclipsing systems is key to understand this behavior. Aims: We aim to investigate the mass-radius relation for low-mass stars and the cause of the deviation of the observed radii in low-mass detached eclipsing binary stars (LMDEB) from theoretical stellar models. Methods: We developed a physical model of the LMDEB system NSVS 10653195 to accurately measure the masses and radii of the components. We obtained several high-resolution spectra in order to fit a spectroscopic orbit. Standardized absolute photometry was obtained to measure reliable color indices and to measure the mean Teff of the system in out-of-eclipse phases. We observed and analyzed optical VRI and infrared JK band differential light-curves which were fitted using PHOEBE. A Markov chain Monte-Carlo (MCMC) simulation near the solution found provides robust uncertainties for the fitted parameters. Results: NSVS 10653195 is a detached eclipsing binary composed of two similar stars with masses of M1 = 0.6402 ± 0.0052 M⊙ and M2 = 0.6511 ± 0.0052 M⊙ and radii of R1 = 0.687+0.017-0.024 R⊙ and R2 = 0.672+0.018-0.022 R⊙. Spectral types were estimated to be K6V and K7V. These stars rotate in a circular orbit with an orbital inclination of i = 86.22 ± 0.61 degrees and a period of P = 0.5607222(2) d. The distance to the system is estimated to be d = 135.2+7.6-7.9 pc, in excellent agreement with the value from Gaia. If solar metallicity were assumed, the age of the system would be older than log (age) ˜ 8 based on the Mbol-log Teff diagram. Conclusions: NSVS 10653195 is composed of two oversized and active K stars. While their radii is above model predictions their Teff are in better agreement with models. Full Tables 1-3 and 7 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/627/A153