The arenavirus Z is a zinc-binding RING protein that has been implicated in multiple functions during the viral life cycle. These roles of Z involve interactions with viral and cellular proteins that remain incompletely understood. In this regard, Z inhibits viral RNA transcription and replication through direct interaction with the viral L polymerase. Here, we defined the L-binding domain of Tacaribe virus (TCRV) Z protein and the structural requirements mediating Z homo-oligomerization. By using site-directed mutagenesis, coimmunoprecipitation, and functional assays, we showed that residues R37, N39, W44, L50, and Y57, located around the zinc coordination site I, play a critical role in the Z-L interaction. We also found that Z protein from either TCRV or the pathogenic Junin virus (JUNV) self-associates into oligomeric forms in mammalian cells. Importantly, mutation of the myristoylation site, the strictly conserved residue G at position 2, severely impaired the ability of both TCRV Z and JUNV Z to self-interact as well as their capacity to accumulate at the plasma membrane, strongly suggesting that Z homo-oligomerization is associated with its myristoylation and cell membrane targeting. In contrast, disruption of the RING structure or substitution of W44 or N39, which are critical for L protein recognition, did not affect Z self-binding. Overall, the data presented here indicate that homo-oligomerization is not a requirement for Z-L interaction or Z-mediated polymerase activity inhibition.