Would a zealot barbarian’s divine fury trigger during an opportunity attack?

The Path of the Zealot barbarian (Xanathar’s Guide to Everything, p. 11) gets the Divine Fury feature at level 3, which states:

At 3rd level, while you’re raging, the first creature you hit on each of your turns with a weapon attack takes extra damage equal to 1d6 + half your barbarian level. The extra damage is necrotic or radiant; you choose the type of damage when you gain this feature.

Does it work like the Rogue’s Sneak attack, in that it can trigger on opportunity attacks, since it’s a different turn? Or does the "on each of your turns" bit make it not work.