The noncentrosymmetric superconductor Mo₃Rh₂N, with T_c = 4.6 K, adopts a β-Mn-type structure (space group P4₁32), similar to that of Mo₃Al₂C. Its bulk superconductivity was characterized by magnetization and heat-capacity measurements, while its microscopic electronic properties were investigated by means of muon-spin rotation and relaxation (μSR). The low-temperature superfluid density, measured via transverse-field (TF)-μSR, evidences a fully gapped superconducting state with Δ₀ = 1.73k_BT_c, very close to 1.76k_BT_c, the BCS gap value for the weak-coupling case, and a magnetic penetration depth λ₀=586 nm. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined by zero-field (ZF)-μSR measurements, hints at a preserved time-reversal symmetry in the superconducting state. Both TF- and ZF-μSR results evidence a spin-singlet pairing in Mo₃Rh₂N.