The noncentrosymmetric superconductor Mo3Rh2N, with T-c = 4.6 K, adopts a beta-Mn-type structure (space group P4(1)32), 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 (mu SR). The low-temperature superfluid density, measured via transverse-field (TF)-mu SR, evidences a fully gapped superconducting state with Delta(0) = 1.73k(B)T(c), very close to 1.76k(B)T(c), the BCS gap value for the weak-coupling case, and a magnetic penetration depth lambda(0) = 586 nm. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined by zero-field (ZF)-mu SR measurements, hints at a preserved time-reversal symmetry in the superconducting state. Both TF- and ZF-mu SR results evidence a spin-singlet pairing in Mo3Rh2N.