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We consider the quench of an atomic impurity via a single Rydberg excitation in a degenerate Fermi gas. The Rydberg interaction with the background gas particles induces an ultralong-range potential that binds particles to form dimers, trimers, tetramers, etc. Such oligomeric molecules were recently observed in atomic Bose-Einstein condensates. Understanding the effects of a correlated background on molecule formation, absent in bosonic baths, is crucial to explain ongoing experiments with Fermi gases. In this work we demonstrate with a functional determinant approach that quantum statistics and fluctuations have clear observable consequences. We show that the occupation of molecular states is predicated on the Fermi statistics, which suppresses molecular formation in an emergent molecular shell structure. At high gas densities this leads to spectral narrowing, which can serve as a probe of the quantum gas thermodynamic properties. Rydberg excitations in Fermi gases go beyond traditional impurity problems, creating an opportunity for studies of mesoscopic interactions in synthetic quantum matter.