We present high-resolution long-slit spectroscopy of a Balmer-dominated shock in the northeastern limb of the Cygnus Loop with the Subaru high dispersion spectrograph. By setting the slit angle along the shock normal, we investigate variations of the flux and profile of the H-alpha line from preshock to postshock regions with a spatial resolution of about 4 times 10^{15} cm. The H-alpha line profile can be represented by a narrow (28.9+/-0.7 km/s) Gaussian in a diffuse region ahead of the shock, i.e., a photoionization precursor, and narrow (33.1+/-0.2 km/s) plus broad (130-230 km/s) Gaussians at the shock itself. We find that the width of the narrow component abruptly increases up to 33.1+/-0.2 km/s, or 38.8+/-0.4 km/s if we eliminate projected emission originating from the photoionization precursor, in an unresolved thin layer (< 4 times 10^{15} cm at a distance of 540 pc) at the shock. We show that the sudden broadening can be best explained by heating via damping of Alfven waves in a thin cosmic-ray precursor, although other possibilities are not fully ruled out. The thickness of the cosmic-ray precursor in the Cygnus Loop (a soft gamma-ray emitter) is an order of magnitude thinner than that in Tycho's Knot g (a hard gamma-ray emitter), which may be caused by different energy distribution of accelerated particles between the two sources. In this context, systematic studies might reveal a positive correlation between the thickness of the cosmic-ray precursor and the hardness of the cosmic-ray energy distribution.