Intermediate mass black holes (IMBHs), with masses between 100 to 10^5 M_odot, represent the link between stellar mass black holes and the supermassive black holes that reside in galaxy centers. While IMBHs are crucial to our understanding of black hole seed formation, black holes of less than approx 10^4 M_odot eluded detection by traditional searches. Observations of the infrared coronal lines (CLs) offer us one of the most promising tools to discover IMBHs in galaxies. We have modeled the infrared emission line spectrum that is produced by gas photoionized by an AGN radiation field and explored for the first time the dependence of the infrared CL spectrum on black hole mass over the range of 10^2 M_odot to 10^8 M_odot. We show that infrared CLs are expected to be prominent in the spectra of accreting IMBHs and can potentially be a powerful probe of the black hole mass in AGNs. We identify key emission line ratios in the 1-30 mu m range that are most sensitive to black hole mass. While variations in accretion rate and the physical parameters of the gas can also affect the CL spectrum, we demonstrate that the effect of black hole mass is likely to be the most dramatic over the mass range explored in our models. With the unprecedented sensitivity of JWST, a large number of CLs will be detectable for the first time, providing important insight into the existence and properties of IMBHs in the local universe, potentially revolutionizing our understanding of this class of object.