Meniscal injuries caused by trauma, degeneration, osteoarthritis, or other diseases always result in severe joint pain and motor dysfunction. Due to the unique anatomy of the human meniscus, the damaged meniscus lacks the ability to repair itself. Moreover, current clinical treatments for meniscal injuries, including meniscal suturing or resection, have significant limitations and drawbacks. With developments in tissue engineering, biopolymer scaffolds have shown promise in meniscal injury repair. They act as templates for tissue repair and regeneration, interacting with surrounding cells and providing structural support for newly formed meniscal tissue. Biomaterials offer tremendous advantages in terms of biocompatibility, bioactivity, and modifiable mechanical and degradation kinetics. In this study, the preparation and composition of meniscal biopolymer scaffolds, as well as their properties, are summarized. The current status of research and future research prospects for meniscal biopolymer scaffolds are reviewed in terms of collagen, silk, hyaluronic acid, chitosan, and extracellular matrix (ECM) materials. Overall, such a comprehensive summary provides constructive suggestions for the development of meniscal biopolymer scaffolds in tissue engineering.