We report on observing a long-wavelength band in low-temperature photoluminescence (PL) spectrum of quaternary Al0.22In0.02Ga0.76N/Al0.38In0.01Ga0.61N multiple quantum wells (MQWs), which were grown over sapphire substrates by a pulsed atomic-layer epitaxy technique. By comparing the excitation-power density and temperature dependence of the PL spectra of MQWs and bulk quaternary AlInGaN layers, we show this emission band to arise from the carrier and/or exciton localization at the quantum well interface disorders. PL data for other radiative transitions in MQWs indicate that excitation-dependent spectra position is determined by screening of the built-in electric field.