Abstract With advancements in medical imaging technology, colour medical images make lesion diagnosis more intuitive. However, when transmitting these high‐capacity images, doctors and researchers must not only address the challenges of storage and transmission efficiency but also guard against unauthorized access and data security risks. To address these issues, a revolutionary approach for colour medical image compression encryption based on compressive sensing and deoxyribonucleic acid (DNA) coding operation is introduced in this study. Randomness and sparse optimizations are performed on three floating‐point matrices obtained through discrete wavelet and sparse transforms of plain colour medical images by employing position scrambling and reduced‐stiffness operations. Subsequently, the floating‐point matrices are measured and quantized to generate three 8‐bit integer matrices. Further, pixel‐by‐pixel DNA encoding, DNA‐base scrambling, DNA XOR, and DNA decoding operations are performed to achieve DNA base‐position scrambling and value diffusion. Finally, the regrouped bit planes help yield the compressed encrypted images. A comprehensive analysis of the proposed algorithm's encryption and decryption effectiveness, compression performance, and security was conducted. The results show that, with a compression ratio of 0.5, average PSNR = 42.7153 dB and average MSSIM = 0.9779, key space is , average entropy = 7.9986 bits, average histogram variance = 509.53, and the correlation coefficients are close to 0. Moreover, the algorithm shows some immunity to common cryptographic attacks, such as differential, known‐plaintext, noise, and occlusion attacks. Thus, the proposed algorithm addresses the challenges posed by the sensitive nature of patient information and limited storage space.