Fiber-optic sensors suitable for monitoring physiological analyte concentration. An analyte-permeable matrix is disposed in the light path defined by the axial core at one end of an optical fiber segment. The matrix contains an indicator molecule covalently linked to a polymer, preferably methyl methacrylate/methacrylamidopropyltrimethylammonium chloride, N-vinylpyrrolidone/p-aminostyrene, methyl methacrylate/hydroxymethyl methacrylate, methyl methacrylate/N-vinylpyrrolidone, or methyl methacrylate/acrylic acid. In representative embodiments, the polymer is approximately 94:6 mole/mole percent of either methyl methacrylate/methacrylamidopropyltrimethylammonium chloride or N-vinylpyrrolidone/p-aminostyrene copolymer. Drift-free performance is obtained with such sensors having analyte-permeable matrices of significantly less than about 70 microns in thickness. The indicator molecule may be covalently linked to the polymer through an aminoarylalkylamine, such as 4-(aminophenyl)-ethylamine or 4-(aminophenyl)-propylamine.