The use of in vitro cultures in plant breeding allows for obtaining cultivars with improved properties. In the case of Stevia rebaudiana Bert., genotypes with an appropriate rebaudioside A/stevioside ratio are desirable. The use of indirect organogenesis allows for the induction of somaclonal variation, which, consequently, results in obtaining variability within the regenerants. The Murashige and Skoog medium containing 4.0 mg × dm−3 6-benzylaminopurine (BAP), 2.0 mg × dm−3 1-naphthaleneacetic acid (NAA), and 2.0 mg × dm−3 2,4-dichlorophenoxyacetic acid (2,4-D) resulted in obtaining plants that were biochemically and genetically diverse. The obtained regenerants were characterized by an increased content of rebaudioside A and a better rebaudioside A/stevioside ratio. Genetic analysis using SCoT (start-codon-targeted) markers showed their diversity at the molecular level. Moreover, this study showed that genotype multiplication through six subsequent re-cultures does not cause variability at the genotype level and does not affect the steviol glycoside profile. This study is the first report on obtaining genotypes with higher rebaudioside A content and a more attractive rebaudioside A to stevioside ratio through the use of in vitro cultures. The improved regenerants can be used as parents in hybridization programs or directly as valuable new genotypes.