The decoding of the human genome, completed two decades ago, marked a revolutionary moment in biology by introducing a vast amount of data. This avalanche of information presented several computational challenges. Machine Learning has become the dominant method to address these challenges, with Natural Language Processing playing a significant role and offering promising results. In this systematic review, we will explore the application of Machine Learning and Natural Language Processing to the study of biological data. On the one hand, Machine Learning is widely used in Artificial Intelligence to improve automation, carry out tasks that require no human interaction, and perform analytical and physical activities. It helps advance our understanding of biology and improve healthcare and drug development processes in bioinformatics. On the other hand, improved machine-human language interaction is the aim of Natural Language Processing. Its three main goals are character sequence processing, pattern recognition, and algorithm development. The use of Natural Language Processing is becoming increasingly important for the analysis of omics data using both modern and conventional Machine Learning models, underscoring the necessity for a systematic review. In this work, 82 studies were included following the PRISMA guidelines, sourced from PubMed, Scopus and IEEE Xplore on April 4th, 2023. The evaluation of the publications was based on the type of the studied biological data and the employed NLP techniques. Through our in-depth exploration of NLP approaches, we highlight their significance and potential in advancing the field of bioinformatics.