  A $\gamma\gamma$ angular correlation experiment has been performed to
investigate the low-energy states of the nucleus $^{98}$Mo. The new data,
including spin assignments, multipole mixing ratios and lifetimes reveal
evidence for shape coexistence and mixing in $^{98}$Mo, arising from a proton
intruder configuration. This result is reproduced by a theoretical calculation
within the proton-neutron interacting boson model with configuration mixing,
based on microscopic energy density functional theory. The microscopic
calculation indicates the importance of the proton particle-hole excitation
across the Z=40 sub-shell closure and the subsequent mixing between spherical
vibrational and the $\gamma$-soft equilibrium shapes in $^{98}$Mo.
