FAM46C, frequently mutated in multiple myeloma (MM), has recently been shown to encode a non‐canonical poly(A) polymerase (ncPAP). However, its target mRNAs and its role in MM pathogenesis remain mostly unknown. Using CRISPR‐Cas9 technology and gene expression analysis, we found that the inactivation of FAM46C in MM down‐regulates immunoglobulins (Igs) and several mRNAs encoding ER‐resident proteins, including some involved in unfolded protein response and others that affect glycosylation. Interestingly, we show that FAM46C expression is induced during plasma cell (PC) differentiation and that Ig mRNAs encoding heavy and light chains are substrates of the ncPAP, as revealed by poly(A) tail‐length determination assays. The absence of the ncPAP results in Ig mRNA poly(A) tail‐shortening, leading to a reduction in mRNA and protein abundance. On the other hand, loss of FAM46C up‐regulates metastasis‐associated lncRNA MALAT1 and results in a sharp increase in the migration ability. This phenotype depends mainly on the activation of PI3K/Rac1 signalling, which might have significant therapeutic implications. In conclusion, our results identify Ig mRNAs as targets of FAM46C, reveal an important function of this protein during PC maturation to increase antibody production and suggest that its role as a tumour suppressor might be related to the inhibition of myeloma cell migration.