The development of reactive powder concretes based on alkali-activated cements for the construction and protection of critical infrastructure is of worldwide importance for improving the safety of their exploitation. The factors influencing the kinetics of strength gain and drying shrinkage of reactive powder concretes using sodium silicate pentahydrate as an alkaline activator were determined. It was shown that increasing the ratio of alkali-activated cement to sand from 1/3 to 1/1 and using the activator in the liquid state increased the concrete strength gain: the compressive strength was 52.3 MPa, 85.0 MPa, 100.6 MPa, and 116.7 MPa at 1, 3, 28, and 90 d. The ratio of compressive strength to flexural strength was in the range of 5.3…5.9 after 28 d, indicating high fracture toughness of the concrete. Higher content of alkali-activated cement caused a decrease in the influence of sand granulometry on concrete strength. This was due to “floating” placement of aggregate in the cement matrix. The introduction of fine calcite as an additive ensured to reduce the shrinkage of concrete by 1.3…1.5 times at 90 d due to the densification of the microstructure and the intensification of crystallization processes. The implementation of these measures resulted in high strength alkali-activated cement reactive powder concrete of strength class C80/95, high fracture toughness, and reduced drying shrinkage.