While the Standard Model of particle physics does not include free particles with fractional charge, experimental searches have not ruled out their existence. We report results from the Cryogenic Dark Matter Search (CDMS II) experiment that give the first direct-detection limits for cosmogenically-produced relativistic particles with electric charge lower than $e$/6. A search for tracks in the six stacked detectors of each of two of the CDMS II towers found no candidates, thereby excluding new parameter space for particles with electric charges between $e$/6 and $e$/200.