The influence of the conditions of the formation of chitosan hydrogels crosslinked with glutaraldehyde (GA) or genipin (the polysaccharide molecular weight, pH level, and concentration of the chitosan solution) on the gel time and the properties of biopolymer scaffolds for tissue engineering obtained by the freeze-drying of hydrogels was studied. The resulting scaffolds had different structures (morphology, degree of anisotropy, average pore size) and moisture-retaining capacities. The cytotoxicity of biodegradable scaffolds based on chitosan with a low content of genipin and GA was studied for the first time. Using the L929 mouse fibroblasts model line, we demonstrated that scaffolds based on chitosan with a molecular weight of 320 and 190 kDa crosslinked with genipin and GA (0.005 and 0.01 mol/mol of chitosan amino groups) are biocompatible. Using confocal laser microscopy, we demonstrated that the cells are uniformly distributed in all scaffold samples and they successfully grew and proliferated when cultured in vitro for 4 days.