The modern applications, such as smart cities, connected homes, and crisis management systems, has driven the emergence of the edge-cloud continuum to enable data processing to occur closer to the source, reducing latency and enhancing data processing efficiency. However, due to the distributed nature of edge nodes and cloud environments, data security remains a critical concern. Malicious actors may intercept or eavesdrop on communication channels between edge devices and the cloud. DNA computing, a groundbreaking security concept inspired by biological DNA, offers a promising solution to address these security challenges. This paper proposes a DNA-based cryptographic method for secure data transfer and communication in edge-cloud computing environments. The research also examines into various data security threats in the edge-cloud continuum and explores potential countermeasures.