Multichannel blind audio source separation aims to recover the latent sources from their multichannel mixtures without supervised information. One state-of-the-art blind audio source separation method, named independent low-rank matrix analysis (ILRMA), unifies independent vector analysis (IVA) and nonnegative matrix factorization (NMF). However, the spectra matrix produced from NMF may not find a compact spectral basis. It may not guarantee the identifiability of each source as well. To address this problem, here we propose to enhance the identifiability of the source model by a minimum-volume prior distribution. We further regularize a multichannel NMF (MNMF) and ILRMA respectively with the minimum-volume regularizer. The proposed methods maximize the posterior distribution of the separated sources, which ensures the stability of the convergence. Experimental results demonstrate the effectiveness of the proposed methods compared with auxiliary independent vector analysis, MNMF, ILRMA and its extensions.