The strengthening and stabilization of damaged compressed masonry columns with composites based on fabrics of high-strength fibers and epoxy resin, or polymer-modified cement mixtures, belongs to novel, partially non-invasive and reversible progressive methods. The stabilizing and reinforcing effect of these fabrics significantly applies to masonry structures under concentric compressive loading whose failure mechanism is characterized by the appearance and development of vertical tensile cracks accompanied by an increase in horizontal masonry strain. During the appearance of micro and hairline cracks (10−3 to 10−1 mm), the effect of non-pre-stressed wrapping composite is very small. The favorable effect of passive wrapping is only intensively manifested after the appearance of cracks (10−1 mm and bigger) at higher loading levels. In the case of “optimum” reinforcement of a masonry column, the experimental research showed an increase in vertical displacements δy (up to 247%), horizontal displacements δx (up to 742%) and ultimate load-bearing capacity (up to 136%) compared to the values reached in unreinforced masonry columns. In the case of masonry structures in which no intensive “bed joint filler–masonry unit” interaction occurs, e.g., in regular coursed masonry with little differences in the mechanical characteristics of masonry units and the binder, the reinforcing effect of the fabric applies only partially.