According to the Georgia Tech biology website, fermentation occurs in the cytoplasm of both prokaryotic and eukaryotic cells. Fermentation occurs after gycolysis, which is the breakdown of glucose into pyruvate, and is necessary to regenerate NAD+ molecules so that the cell can continue to make ATP.
Prokaryotic cells do not have membrane-bound organelles, so all metabolic processes must occur in the cytoplasm. In eukaryotic cells, pyruvate from the glycolysis pathway is typically transported into the mitochondria and the citric acid cycle. However, this can only occur in the presence of oxygen. Therefore, eukaryotic cells utilize lactic acid or ethanol fermentation in anaerobic conditions.