We developed a surface-enhanced Raman scattering (SERS)-active plasmonic core-satellite nanostructure and incorporated it into a membrane filter-integrated microfluidic device for continuous monitoring of molecules in solution. The core-satellite nanostructures were fabricated by immobilizing a high number density of gold nanoparticles (AuNPs) on silica beads.to create many nanogaps among the AuNPs. The sizes of the nanogaps were fine-tuned by adding a silver (Ag) shell to optimize the SERS activity. In addition, citrate molecule, the capping agent of the nanoparticles, was displaced by alkali halides. The displacement not only reduced the SERS signals of citrate but also enhanced the adsorption of target molecules. The alkali halide-treated core-satellite nanostructures were accumulated onto a membrane filter integrated into a microfluidic device, serving as a uniform and sensitive SERS substrate. By increasing the volume of the sample solution flowing through the membrane filter, we increased the number of molecules adsorbed to the nanostructures, amplifying the intensities of their characteristic Raman peaks. Our microfluidic SERS device demonstrated continuous SERS detection of malachite green at a concentration as low as 500 fM. In summary, while various core-satellite nanostructures and microfluidic SERS devices have been reported, the integration of the membrane filter-containing microfluidic device with the core-satellite nanostructures facilitated sensitive and continuous molecule detection in our study.