We present the microscopic properties of superconducting state in ${\text{Mo}}_{3}{\text{Sb}}_{7}$ $({T}_{c}=2.2\text{ }\text{K})$ using muon-spin rotation measurements. The zero-field-cooled and field-cooled (FC) data with an applied transverse field of 40 mT reveal an irreversibility in the muon relaxation rates and precessional frequencies below 2 K. We have also found an anomaly around 0.5 K, which may be related to a process of the vortex melting or some change in vortex-lattice symmetry. The temperature dependence of FC muon relaxation rate can be analyzed using a phenomenological double-gap $s$-wave model. The observation of a nonlinear field dependence of the muon relaxation rate is consistent with the occurrence of two superconducting gaps. Moreover, the magnetic penetration depth $\ensuremath{\lambda}$, coherence length $\ensuremath{\xi}$, superconducting carrier density ${n}_{s}$, and effective-mass enhancement ${m}^{\ensuremath{\ast}}$ have been found to be $\ensuremath{\lambda}\ensuremath{\approx}665\text{ }\text{nm}$, $\ensuremath{\xi}\ensuremath{\approx}12.5\text{ }\text{nm}$, ${n}_{s}\ensuremath{\approx}1.2\ifmmode\times\else\texttimes\fi{}{10}^{27}\text{ }\text{carriers}/{\text{m}}^{3}$, and ${m}^{\ensuremath{\ast}}\ensuremath{\approx}18.7{m}_{e}$, respectively.