Music therapy is an alternative medicine used to increase the cognitive, emotional, social, or physical health of individuals over the past decades. Music therapy is most successful globally, where personalized and adequate stimuli are provided by therapists to stimulate the human brain. Traditional music therapy techniques are often limited by cost, expertise, availability, and so on. In recent years, the advancement of generative Artificial Intelligence (AI) technologies has aided in understanding general mental well-being via AI-driven music generation systems. Hence, different research on music generation systems using AI is employed to enhance music therapy. This paper presents a comprehensive review of prevailing generative AI-based music generation systems and highlights the performance of each strategy. The prevailing generative AI-based music generation approaches are categorized into Long-Short Term Memory (LSTM)-based, Variational Autoencoder (VAE)-based, Generative Adversarial Networks (GAN)-based, other deep learning-based and machine learning-based music generation systems. Here, 25 research articles are taken for categorization and the fundamental components are outlined. Moreover, the analysis proved that the deep learning-based music generation system is the most used approach, Python tools are widely utilized, and accuracy is the most used evaluation parameter.