Within the HEALTHGRAIN diversity screen, the variability of the contents of dietary fiber (DF) and components thereof was studied in wheat. Furthermore, the contribution of genotype and environment to this variability was estimated. The levels of total DF (TDF), total nonstarch polysaccharide (TOTNSP), water-extractable nonstarch polysaccharide (WENSP), total arabinoxylan (TOTAX), lignin, and beta-glucan in whole meal, flour, and/or bran varied approximately 1.8-fold. The highest variability was observed for the water-extractable arabinoxylan (WEAX) level in flour and bran (approximately 3.7-fold). Genotype and environment contributed to a similar extent to the variability in TDF, TOTNSP, and TOTAX content in wheat. The observed relatively high impact of genotype-environment interaction suggests that the levels of these constituents are weak breeding parameters. The WENSP level is a more stable parameter as the effect of the interaction term was much less than the impact of genotype. For TOTAX and WEAX in flour, WEAX in bran, beta-glucan in whole meal, and extract viscosity, wheat genotype determined approximately 50% or higher of the variation observed, whereas the impact of the genotype-environment interaction was relatively low. These findings suggest that the health-related and technological functionality of wheat can be directed to a certain extent by selection of appropriate wheat varieties.