A vital challenge in using imprinted membranes for selective sensing is their non-specific adsorption (NSA). In this study, a novel, rapid, and green approach of NSA-free molecularly imprinted membrane (MIM) preparation was proposed. Sodium alginate was employed as a functional polymer (to interact with the template) and as a membrane matrix, then cross-linked with calcium before template removal to block the unreacted groups, followed by exposure to phosphate to chelate any remaining sites. Unlike the non-imprinted membrane (NIM), which is prepared similarly to MIM and lacks the template cavities, the MIM demonstrated exceptional imprinting factor (IF) (Q(NIM) approximate to 0 mg/g) compared to the initial IF of around 4 before NSA suppress, and a selectivity factor over 10 times greater than that of existing MIMs in the literature. The NSA-free MIM was used as a ready-to-use sensor for spectro-fluorescence and smartphone-based fluorescence detection of tetracycline (TC), achieving detection limits of 0.005 mg/L and 0.015 mg/L, respectively, which were below the maximal acceptable concentrations of TC in real samples. The detection of TC in milk and honey samples using the NSA-free MIM showed significant recoveries (86-101%) compared to those found by MIM before NSA supress (114-122%). The proposed methodology serves as an inspiration for extending NSA removal strategies to other MIMs based on various anionic polymers, including carboxylate, sulfonate, phosphonate, and phenolate anionic groups.