Three-dimensional bioprinting has rapidly paralleled many biomedical applications and assisted in advancing the printing of complex human organs for a better therapeutic practice. The objective of this systematic review is to highlight evidence from the existing studies and evaluate the effectiveness of using natural-based bioinks in skin regeneration and wound healing. A comprehensive search of all relevant original articles was performed based on prespecified eligibility criteria. The search was carried out using PubMed, Web of Science, Scopus, Medline Ovid, and ScienceDirect. Eighteen articles fulfilled the inclusion and exclusion criteria. The animal studies included a total of 151 animals with wound defects. A variety of natural bioinks and skin living cells were implanted in vitro to give insight into the technique through different assessments and findings. Collagen and gelatin hydrogels were most commonly used as bioinks. The follow-up period ranged between one day and six weeks. The majority of animal studies reported that full wound closure was achieved after 2–4 weeks. The results of both in vitro cell culture and in vivo animal studies showed the positive impact of natural bioinks in promoting wound healing. Future research should be focused more on direct the bioprinting of skin wound treatments on animal models to open doors for human clinical trials.