  Mobility edge, a critical energy separating localized and extended
excitations, is a key concept for understanding quantum localization.
Aubry-Andr\'{e} (AA) model, a paradigm for exploring quantum localization, does
not naturally allow mobility edges due to self-duality. Using the
momentum-state lattice of quantum gas of Cs atoms to synthesize a nonlinear AA
model, we provide experimental evidence for mobility edge induced by
interactions. By identifying the extended-to-localized transition of different
energy eigenstates, we construct a mobility-edge phase diagram. The location of
mobility edge in the low- or high-energy region is tunable via repulsive or
attractive interactions. Our observation is in good agreement with the theory,
and supports an interpretation of such interaction-induced mobility edge via a
generalized AA model. Our work also offers new possibilities to engineer
quantum transport and phase transitions in disordered systems.
