In its orthorhombic T_d polymorph, MoTe₂ is a type-II Weyl semimetal, where the Weyl fermions emerge at the boundary between electron and hole pockets. Non-saturating magnetoresistance and superconductivity were also observed in T_d-MoTe₂. Understanding the superconductivity in T_d-MoTe₂, which was proposed to be topologically non-trivial, is of eminent interest. Here, we report high-pressure muon-spin rotation experiments probing the temperature-dependent magnetic penetration depth in T_d-MoTe₂. A substantial increase of the superfluid density and a linear scaling with the superconducting critical temperature T_c is observed under pressure. Moreover, the superconducting order parameter in T_d-MoTe₂ is determined to have 2-gap s-wave symmetry. We also exclude time-reversal symmetry breaking in the superconducting state with zero-field μSR experiments. Considering the strong suppression of T_c in MoTe₂ by disorder, we suggest that topologically non-trivial s⁺⁻ state is more likely to be realized in MoTe₂ than the topologically trivial s⁺⁺ state.