Muon spin relaxation and rotation (muSR) measurements have been performed to study the superconducting and magnetic properties of Nb2PdS5. Zero-field muSR data show that no sizeable spontaneous magnetization arises with the onset of superconductivity in Nb2PdS5 which indicates that the time reversal symmetry is probably preserved in the superconducting state of this system. A strong diamagnetic shift is observed in the transverse-field muSR data practically ruling out a dominant triplet-pairing superconducting state in Nb2PdS5. The temperature dependence of magnetic penetration depth evidences the existence of a single s-wave energy gap with a gap value of 1.07(4) meV at zero temperature. The gap to Tc ratio, 2.02(9), indicates that Nb2PdS5 should be considered as a moderately strong-coupling superconductor. The magnetic penetration depth at zero temperature is 785(20) nm, indicating a very low superfluid density consistent with the quasi-one-dimensional nature of this system.