Early-age masonry structures require temporary support until they achieve full strength. Nevertheless, there is a limited understanding of the properties of freshly laid masonry and the design of newly constructed, unsupported masonry walls. This situation has led to numerous instances of structural damage and injuries to workers, prompting conservative construction bracing techniques. This paper presents comprehensive experimental studies on early-age mortar cubes and masonry prisms to assess the effects of curing time on the compressive properties of masonry assemblies, which is necessary for the design of temporary bracing. The change in modulus of elasticity and compressive strength of masonry prisms and mortar with curing time has been experimentally assessed. The results indicate that the compressive strength of freshly cast mortar cubes is relatively insignificant until approximately 24 h after construction, when it was observed to increase logarithmically. Regarding the performance perspective, the compressive strength of early-age masonry prisms is inconsiderable, less than 15% of full strength during the first day after construction. By contrast, regarding the life safety perspective, the compressive properties of a mortar joint within a masonry assembly (which is of more practical interest) appear to have no effect on the failure strength of concrete masonry prisms over the range of ages tested. The failure modes of the early-age mortar cubes and early-age masonry prism samples depend on the curing time, and different failure modes occurred before and after the start of the primary hydration phase, which is 20.8 h after construction. It is anticipated that the proposed research will provide valuable material properties leading to efficient design of control devices (e.g., temporary bracing) and improved guidelines for concrete-block masonry construction.