In the past, asbestos siding, roofing, and ceiling sheets became more popular than conventional materials due to their high strength-to-weight ratio, durability, and low cost. However, it was later identified that most types of asbestos are carcinogenic and are responsible for major lethal diseases. In terms of developing a substitute for asbestos, different alternative organic fibers have been investigated as sustainable solutions. Therefore, this article reviewed the usability of organic fibers from wood, banana, bamboo, and coconut coir, which are locally available and abundant in the region, as a substitute for asbestos in the fiber cement industry in Sri Lanka. The quantitative physicomechanical properties of organic fiber and fiber cement composites were evaluated, and the effect of treatment methods on durability was discussed. The previous literature revealed that organic fiber cement thin sheets have comparable mechanical properties in comparison to composites reinforced with asbestos. Furthermore, this study found that these organic-fiber-based composites are energy-efficient and have improved fire resistance. However, the long-term performance is questionable. Hence, further studies on fiber treatment methods and composite durability are needed. Additionally, a comprehensive cost analysis of organic fiber cement composite is recommended to introduce organic fibers into commercial products.