The recently developed Multi-Channel Factor Analysis (MFA) is a method for extracting a latent low-dimensional signal that is present across multiple channels and corrupted by unobserved single-channel interference and idiosyncratic noise. In MFA, only the channel structure and dimensionality of the signal and interference subspaces are specified in advance, which raises the concern that the signal, interference, and noise covariances may not be uniquely determined by the observation model. This paper presents necessary and sufficient conditions on the channel sizes and subspace dimensions to guarantee the identifiability of MFA, ensuring that the second-order spatial properties of the latent components can, in principle, be recovered from the multi-channel observations.