We report a comprehensive study of the noncentrosymmetric superconductor Mo₃P. Its bulk superconductivity, with T_c = 5.5 K, was characterized via electrical-resistivity, magnetization, and heat-capacity measurements, while its microscopic electronic properties were investigated by means of muon-spin rotation/relaxation (μSR) and nuclear magnetic resonance (NMR) techniques. In the normal state, NMR relaxation data indicate an almost ideal metallic behavior, confirmed by band-structure calculations, which suggest a relatively high electron density of states, dominated by the Mo 4d orbitals. The low-temperature superfluid density, determined via transverse-field μSR and electronic specific heat, suggest a fully gapped superconducting state in Mo₃P, with zero-temperature gap Δ₀ = 0.83 meV, the same as the BCS gap value in the weak-coupling case, and a zero-temperature magnetic penetration depth λ₀ = 126nm. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined from zero-field μSR measurements, indicates a preserved time-reversal symmetry in the superconducting state of Mo₃P and, hence, spin-singlet pairing.