We report infrared spectroscopic observations of a large, well-defined sample of main-sequence, single-lined spectroscopic binaries in order to detect the secondaries and derive the mass ratio distribution of short-period binaries. The sample consists of 51 Galactic disk spectroscopic binaries found in the Carney and Latham high-proper-motion survey, with primary masses in the range of 0.6--0.85 msun. Our infrared observations detect the secondaries in 32 systems, two of which have mass ratios, q=M_2/M_1, as low as ~0.20. Together with 11 systems previously identified as double-lined binaries by visible light spectroscopy, we have a complete sample of 62 binaries, out of which 43 are double-lined. The mass ratio distribution is approximately constant over the range q=1.0 to 0.3. The distribution appears to rise at lower q values, but the uncertainties are sufficiently large that we cannot rule out a distribution that remains constant. The mass distribution derived for the secondaries in our sample, and that of the extra-solar planets, apparently represent two distinct populations.