The invention relates to a machine for labeling “blank-labeled” cryogenically-frozen vials or ampoules, which contain heat-labile biological materials, and to which a laser-light sensitive material had been applied prior to freezing. Accordingly, the machine has been designed to maintain the integrity of the biological materials throughout all phases of the labeling process. The machine generally comprises a master control system; a programmable user interface; a frame; cryogenic freezer assemblies, for keeping the vials at the required low temperatures; an infeed assembly, configured to receive and position blank-labeled cryogenic vials; a cryostatic labeling/quality control tunnel, wherein the vials are maintained at the required temperature, labeled by laser ablation, and checked for quality; and, an outfeed assembly. The machine further comprises a means for transporting the vials from the infeed assembly to the tunnel, and from the tunnel to the outfeed assembly. Vials labeled according to the instant disclosure are ultimately manually or automatically loaded into cryogenic shipping containers.