Plant endophytes are known to alter the profile of secondary metabolites in plant hosts. In this study, we identified the main bacterial and fungal representatives of the wild grape Vitis amurensis Rupr. microbiome and investigated a cocultivation effect of the 14 endophytes and the V. amurensis cell suspension on biomass accumulation and stilbene biosynthesis. The cocultivation of the V. amurensis cell culture with the bacteria Agrobacterium sp., Bacillus sp., and Curtobacterium sp. for 2 weeks did not significantly affect the accumulation of cell culture fresh biomass. However, it was significantly inhibited by the bacteria Erwinia sp., Pantoea sp., Pseudomonas sp., and Xanthomonas sp. and fungi Alternaria sp., Biscogniauxia sp., Cladosporium sp., Didymella sp. 2, and Fusarium sp. Cocultivation of the grapevine cell suspension with the fungi Didymella sp. 1 and Trichoderma sp. resulted in cell death. The addition of endophytic bacteria increased the total stilbene content by 2.2–5.3 times, while the addition of endophytic fungi was more effective in inducing stilbene accumulation by 2.6–16.3 times. The highest content of stilbenes in the grapevine cells cocultured with endophytic fungi was 13.63 and 13.76 mg/g of the cell dry weight (DW) after cultivation with Biscogniauxia sp. and Didymella sp. 2, respectively. The highest content of stilbenes in the grapevine cells cocultured with endophytic bacteria was 4.49 mg/g DW after cultivation with Xanthomonas sp. The increase in stilbene production was due to a significant activation of phenylalanine ammonia lyase (PAL) and stilbene synthase (STS) gene expression. We also analyzed the sensitivity of the selected endophytes to eight antibiotics, fluconazole, and trans-resveratrol. The endophytic bacteria were sensitive to gentamicin and kanamycin, while all selected fungal strains were resistant to fluconazole with the exception of Cladosporium sp. All endophytes were tolerant of trans-resveratrol. This study showed that grape endophytes stimulate the production of stilbenes in grape cell suspension, which could further contribute to the generation of a new stimulator of stilbene biosynthesis in grapevine or grape cell cultures.