A search for a new scalar field, called moduli, has been performed using the cryogenic resonant-mass AURIGA detector. Predicted by string theory, moduli may provide a significant contribution to the dark matter (DM) component of our Universe. If this is the case, the interaction of ordinary matter with the local DM moduli, forming the Galaxy halo, will cause an oscillation of solid bodies with a frequency corresponding to the mass of moduli. In the sensitive band of AURIGA, some 100 Hz at around 1 kHz, the expected signal, with Q=△f/f∼10^{6}, is a narrow peak, △f∼1 mHz. Here the detector strain sensitivity is h_{s}∼2×10^{-21} Hz^{-1/2}, within a factor of 2. These numbers translate to upper limits at 95% C.L. on the moduli coupling to ordinary matter (d_{e}+d_{m_{e}})≲10^{-5} around masses m_{ϕ}=3.6×10^{-12} eV, for the standard DM halo model with ρ_{DM}=0.3 GeV/cm^{3}.