In this work, a humidification–dehumidification unit powered by solar energy was designed, constructed, and tested for brackish water desalination. In order to enhance the mass and heat transfer between feedwater and flowing air, 16 layers of wick were used as packing material. The results showed that the daily productivity increased by 28.28% when wick was used. The desalination unit with wick was tested at different temperatures and flowrates of feedwater. High significance positive relation between productivity and feedwater flowrate was found. The proposed system was also tested at a wide range of air flowrate. The results also showed that the peak value of productivity was achieved when the air flowrate was 0.0075 kg/s. It was also found that the daily productivity increased by 31.3% when the feedwater flowrate was increased from 0.114 to 0.171 kg/s when the air flowrate was 0.0075 kg/s.