The paper presents the results of an experimental study of medium-strength concrete for cement floors, performed according to the ASTM C 1579–06 standard test method for evaluating shrinkage cracks. In the process of experimental study the growth of shrinkage cracks development was recorded using a digital camera. Processing of the obtained images of shrinkage cracks was performed, using the cube counting method, and the fractal dimension of cracks was determined. Approbation of the methodology for determining the Minkowski fractal dimension for cracks formed on the concrete surface by processing digital photographs has been carried out. Graphs of dependence of strength change on time according to the results of standard tests of specimens of concrete cubes, graphs of dependence of change of fractal dimension of a crack on time in the process of concrete strength gain are constructed. According to the results of the experimental study the dependence between concrete strength and fractal dimension of cracks was established. A nondestructive method of express control of concrete strength at intermediate age is proposed on the basis of the use of fundamental provisions of fractal mechanics of concrete fracture.