Transparent p–n heterojunctions composed of p-type CuAlOx:Ca and n-type MgZnO thin films are fabricated on indium tin oxide (ITO) coated polyethylene terephthalate (PET) using RF magnetron sputtering at room temperature without additional heat-treatment. The rectifying characteristics of the diodes are observed through the current density–voltage (J–V) curves. The characteristics of the heterojunctions vary with the Mg content in MgZnO. The absolute values of the turn-on voltage and breakdown voltage increase with the Mg content. The diode properties can be designed by adjusting Mg content in the MgZnO layers. The UV responses of the diodes are evaluated by measuring the J–V characteristics under UV irradiation at a wavelength of 365 nm. The absorption decreases with an increase in the Mg content in the diodes. The results show that these transparent diodes can be used as UV detectors on plastics.