Masonry-infilled panels are normally used as partitions or as architectural elements in reinforced concrete (RC) structures. The need for incorporating openings to the walls of a building in order to provide natural lighting and ventilation leads to partial lateral confinement along the height of the column by rigid elements, such as internal partitions and facades. This situation introduces large shear stresses, when the structure is subjected to seismic forces and the columns can be seriously damaged due to captive-column effect. This paper presents the results of analytical and experimental investigations of one-third scaled two-bay two-story RC frames with partial infill in the bottom story and subjected to lateral cyclic loads. A local retrofitting strategy of strengthening RC structural elements with glass fiber reinforced polymer (GFRP) composites was adopted. Test results indicated that the retrofitted frame exhibited significantly higher ultimate strength and stiffness than the control frame (frame without retrofit). Force–deformation relationships, damage patterns, and other characteristics of the frames were also demonstrated. The aim of the GFRP retrofit was to enhance the global performance of the partially infilled structure under seismic action, by preventing the development of captive-column conditions.