Mass excesses of $^{52}$Co and its $(2^+)$ isomer are measured to be $-34361(8)$ keV and $-33974(10)$ keV using isochronous mass spectrometry at CSRe. Referring to the $\beta$-delayed $\gamma$ emissions of $^{52}$Ni, we identified a new excited state in $^{52}$Co and assigned it as the $T=2$, $J^{\pi}=0^+$ isobaric analog state (IAS) of $^{52}$Ni. This state is 135(17) keV less bound than that suggested previously based on the $\beta$-delayed protons of $^{52}$Ni. We find that the mass of this IAS together with those of the IAS's in $^{52}$Fe, $^{52}$Mn, and $^{52}$Cr fit well into the Isobaric Multiplet Mass Equation. An interesting finding from this measurement is that the IAS in $^{52}$Co decays dominantly via $\gamma$ transitions while proton emission is almost negligible. This phenomenon could be due to very low isospin mixing according to the large-scale shell model calculations.