In the approximation of small fluctuations, the spectral density of intrinsic thermal noise limiting the maximal sensitivity of a constant-current SQUID is found in the low-frequency region. The dependence of the signal-to-noise ratio on the SQUID parameters and operating conditions of an interferometer with low-frequency magnetic flux modulation is studied. Estimates are presented for the smallest detectable magnetic flux corrsponding to optimal operating conditions of a SQUID.