Recently, compounds with noncentrosymmetric crystal structure have attracted much attention for providing a rich playground in search for unconventional superconductivity. NbIr₂B₂ is a new member to this class of materials harboring superconductivity below T_c = 7.3(2) K and a very high upper critical field that exceeds Pauli limit. Here we report on muon spin rotation (μSR) experiments probing the temperature and field dependence of effective magnetic penetration depth in this compound. Our transverse-field-μSR results suggest a fully gapped s-wave superconductivity. Furthermore, the estimated high value of the upper critical field is also supplemented by high-field transport measurements. Remarkably, the ratio T_c/λ⁻²(0) obtained for NbIr₂B₂ (∼2) is comparable to those of unconventional superconductors. Zero-field μSR data reveal no significant change in the muon spin relaxation rate above and below Tc, evincing that time-reversal symmetry is preserved in the superconducting state. The presented results will stimulate theoretical investigations to obtain a microscopic understanding of the origin of superconductivity with preserved time-reversal symmetry in this unique noncentrosymmetric system.