The invention relates to a method for the production of resveratrol in cell cultures. The inventive method consists in: incubating a culture of cells which produce resveratrol naturally, in suspension, in the presence of randomly-methylated .beta.-cyclodextrin (RMBCD) with a degree of substitution of between 11 and 13 under conditions that allow resveratrol synthesis and the excretion of same into the culture medium; and, if desired, isolating the resveratrol produced from said culture medium. The resveratrol can be used in the production of pharmaceutical or nutraceutical products.