The physical and chemical properties of organic compounds are deeply affected by the introduction of fluorinated substituents. Perfluorinated and highly fluorinated organic molecules are both hydrophobic and lipophobic. This makes the recognition and the binding of fluorinated molecules extremely difficult to achieve through classical elements of molecular recognition. Here we show that semifluorinated water-soluble block copolymers can generate micellar structures having a fluorous phase-based inner core in aqueous solution. Furthermore, we show that these micelles can be used to encapsulate and bind highly fluorinated molecules through association in the internal fluorous phase (fluorophobic effect). We report that semifluorinated block copolymers can be used for the aqueous solubilization of the widely diffused gaseous anesthetic sevoflurane, thereby suggesting the possibility of the intravenous delivery of this commonly used anesthetic.