Two sturgeon species, Acipenser ruthenus (Linnaeus, 1758) and Acipenser baerii (Brandt, 1869), inhabit the Irtysh basin. In 2018, we received some “atypical” specimens of sturgeon, which were similar to A. ruthenus but had a number of pronounced external differences. The hybrids A. ruthenus × A. baerii, named “oster”, can sometimes be caught in natural habitats in the Ob and the Yenisei rivers. Despite the development of methods for the genetic identification of sturgeons, the molecular genetic characteristics of the hybrids of A. baerii and A. ruthenus have not been carried out. The purpose of this study is to develop a complex of morphological and genetic characters to identify the hybrid of A. ruthenus and A. baerii from the Irtysh River. We used a complex of morphological and genetic methods to compare the putative hybrids with parental species The putative hybrids were similar to A. ruthenus in the number of dorsal scutes, the number of rays in the dorsal and anal fins, the structure of stamens on the first gill arch, and the presence of fringe on the tendrils. The hybrids were similar to A. baerii in size and weight values, the structure of dorsal scutes, the number of lateral and ventral scutes, and the number of gill rakers on the first gill arch. Genotyping of putative hybrids by using the Inter Simple Sequence Repeat (ISSR) markers revealed the presence of sites characteristic of both parental species. The fragment of the control region of mitochondrial DNA in the hybrids matched to that of A. baerii that allowed us to identify females of A. baerii as maternal individuals of the hybrids. Possible causes and factors promoting interspecific hybridization of A. ruthenus and A. baerii were studied. This is the first described fact of the appearance of sturgeon hybrids in the Ob-Irtysh basin. It is necessary to continue monitoring studies to identify the number of these hybrids in the ecological system of the Irtysh River. The data set of morphological characters and genetic methods can be used to identify the hybrids of A. ruthenus and A. baerii.