The level structure of $^{172}$Dy has been investigated for the first time by means of decay spectroscopy following in-flight fission of a $^{238}$U beam. A long-lived isomeric state with $T_{1/2} = 0.71(5)$ s and $K^{\pi} = 8^-$ has been identified at 1278 keV, which decays to the ground-state and $\gamma$-vibrational bands through hindered electromagnetic transitions, as well as to the daughter nucleus $^{172}$Ho via allowed $\beta$ decays. The robust nature of the $K^{\pi} = 8^-$ isomer and the ground-state rotational band reveals an axially-symmetric structure for this nucleus. Meanwhile, the $\gamma$-vibrational levels have been identified at unusually low excitation energy compared to the neighboring well-deformed nuclei, indicating the significance of the microscopic effect on the non-axial collectivity in this doubly mid-shell region. The underlying mechanism of enhanced $\gamma$ vibration is discussed in comparison with the deformed Quasiparticle Random-Phase Approximation based on a Skyrme energy-density functional.