Millimeter sized single crystals of Mo3Sb7 are grown using the self-flux technique and a thorough characterization of their structural, magnetic, thermal and transport properties is reported. The structure parameters for the high-temperature cubic phase and the low-temperature tetragonal phase were, for the first time, determined with neutron single crystal diffraction. Both X-ray powder diffraction and neutron single crystal diffraction at room temperature confirmed that Mo3Sb7 crystallizes in Ir3Ge7-type cubic structure with space group Im-3m. The cubic-tetragonal structure transition at 53K is verified by the peak splitting of (4 0 0) reflection observed by X-ray single crystal diffraction and the dramatic intensity change of (12 0 0) peak observed by neutron single crystal diffraction. The structural transition is accompanied by a sharp drop in magnetic susceptibility, electrical resistivity, and thermopower while cooling. A weak lambda anomaly was also observed around 53K in the temperature dependence of specific heat and the entropy change across the transition is estimated to be 1.80J/molMoK. The temperature dependence of magnetic susceptibility was measured up to 750K and it follows a Curie-Weiss behavior above room temperature. Analysis of the low-temperature magnetic susceptibility suggests a spin gap of 110K around 53K. A typical phonon thermal conductivity was observed in the low temperature tetragonal phase. A glassy phonon thermal conductivity above 53K suggests a structural instability in a wide temperature range. Superconductivity was observed at 2.35K in the as-grown crystals and the dimensionless specific heat jump was determined to be 1.49, which is slightly larger than the BCS value of 1.43 for the weak-coupling limit. ; Comment: 9 pages, 10 figures, accepted for publication in Phys. Rev. B