Hemp (Cannabis sativa L.) is a bast-fiber crop well-known for the great potential to produce sustainable fibers. Nevertheless, hemp fiber quality is a complex trait, and little is known about the phenotypic variability and heritability of fiber quality traits in hemp. The aim of this study is to gain insights into the variability in fiber quality within the hemp germplasm and to estimate the genetic components, environmental components, and genotype-by-environment (G×E) interactions on fiber quality traits in hemp. To investigate these parameters, a panel of 123 hemp accessions was phenotyped for 28 traits relevant to fiber quality at three locations in Europe, corresponding to climates of northern, central, and southern Europe. In general, hemp cultivated in northern latitudes showed a larger plant vigor while earlier flowering was characteristic of plants cultivated in southern latitudes. Extensive variability between accessions was observed for all traits. Most cell wall components (contents of monosaccharides derived from cellulose and hemicellulose; and lignin content), bast fiber content, and flowering traits revealed large genetic components with low G×E interactions and high broad-sense heritability values, making these traits suitable to maximize the genetic gains of fiber quality. In contrast, contents of pectin-related monosaccharides, most agronomic traits, and several fiber traits (fineness and decortication efficiency) showed low genetic components with large G×E interactions affecting the rankings across locations. These results suggest that pectin, agronomic traits, and fiber traits are unsuitable targets in breeding programs of hemp, as their large G×E interactions might lead to unexpected phenotypes in untested locations. Furthermore, all environmental effects on the 28 traits were statistically significant, suggesting a strong adaptive behavior of fiber quality in hemp to specific environments. The high variability in fiber quality observed in the hemp panel, the broad range in heritability, and adaptability among all traits prescribe positive prospects for the development of new hemp cultivars of excellent fiber quality.