The development of alternative meat, such as cultured meat, is of current interest due to its potential to solve various problems common to the livestock industry. Cultured meat is defined as in vitro, lab-grown, or synthetic meat, and is produced through the differentiation and culture of animal cells. To increase the efficiency of this culture veterinary drugs are commonly employed. It is therefore necessary to develop a method that allows the amounts of veterinary drugs, growth-promoting hormones, and antibiotics to be determined in cultured meat, to ultimately ensure an adequate safety profile. In this study, we report the development of an analytical method based on liquid chromatography–tandem mass spectrometry for the simultaneous analysis of various veterinary drugs. Validation of the developed method indicated a high accuracy and precision, in addition to a linearity of 0.9868–0.9999. Using this method, the veterinary drugs present in samples of culture media were analyzed. Importantly, penicillin was detected in the range of 2 to 44,259 mg/L, and no other veterinary drugs were detected. It is therefore expected the implementation of this method will improve the safety profile of the cultured meat market, in addition to securing the safety of new food technologies.