Excited states in the extremely neutron-deficient isotope $^{172}\mathrm{Hg}$ have been established for the first time. The $^{96}\mathrm{Ru}(^{78}\mathrm{Kr},2n)$ reaction was employed to populate excited states in $^{172}\mathrm{Hg}$ with a cross section $\ensuremath{\sigma}\ensuremath{\approx}15$ nb. The highly selective recoil-decay tagging (RDT) technique was used to obtain clean in-beam $\ensuremath{\gamma}$-ray spectra for $^{172}\mathrm{Hg}$. The yrast ground-state band has tentatively been established up to $I=6 \ensuremath{\hbar}$. The data have been interpreted within the framework of total Routhian surface and quasiparticle random phase approximation calculations.