With the rise in antibiotic resistance amongst pathogenic bacteria, the study of antibiotic activity and transport across cell membranes is gaining widespread importance. We present a novel, label-free microfluidic assay that quantifies the permeability coefficient of a broad spectrum fluoroquinolone antibiotic, norfloxacin, across lipid membranes using the UV autofluorescence of the drug. We use giant lipid vesicles as highly controlled model systems to study the diffusion through lipid membranes. Our technique directly determines the permeability coefficient without requiring the measurement of the partition coefficient of the antibiotic.