Biotechnological methods prevent the destruction of natural populations of medicinal plants due to climate change and developing agriculture. This study evaluates the effects of in vitro pretreatment with two types of silver-containing amino acid nanofibers (NF-1%Ag and NF1-Ag salt) on the drought tolerance of ex vitro soil-adapted Steviia rebaudiana Bertoni. The duration of the drought was five days. The data suggested that the pretreatment with the studied nanofibers during plant propagation enhanced the plant tolerance to drought stress manifested in a smaller decrease in plant biomass accumulation and a smaller increase in sugar content. The pretreatment with the two tested nanoparticles of well-watered plants increased the leaf fresh biomass accumulation of the ex vitro-adapted S. rebaudiana compared to the untreated WW control plants. The highest values were reported at 10 mg L−1 NF1-Ag salt. Five days of drought led to a decrease in the leaf fresh biomass compared to the WW plants, with the recorded lowest reduction again at 10 mg L−1 NF1-Ag salt. These observations correlate with antioxidant activity improvement. The results show that adding 10 mg L−1 NF1-Ag salt to the MS medium led to higher ex vitro-adapted S. rebaudiana resistance to water deficit than 100 mg L−1. This paper discusses the impact of the selected nanofibers on parameters characterizing plant growth and antioxidant activity of drought-stressed ex vitro-adapted Stevia rebaudiana plants.