We report on the absorption measurements of the liquid-filled pure-silica microstructured optical fibers. The measurements concentrate on spectroscopic analysis of the water solutions of a cationic dye, oxazine 725 perchlorate which, when filling the fiber, demonstrates much stronger absorption signals than observed in bulk with regular cuvettes. The effect is also seen in another cationic dye, but not in anionic dyes. Our investigations reveal that the effect originates from the adsorption of the dye molecules on the fiber inner walls. This effect also significantly enhances the sensitivity of spectroscopic measurements enabling the detection of molecules at very low concentrations. In particular, the detection of a 1 nM concentration of oxazine 725 perchlorate was demonstrated.