That depends on if it is casting a spell, or granting a spell-like-effect
To cast an actual spell from an item, it requires your concentration. This is specified on page 141 of the DMG
(…) The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration.
This rule would be used in the case of an item such as a Staff of Fire, which allows you to use it to cast the spell Wall of Fire (which requires concentration).
However, to cite the specific example you gave of a Ring of Invisibility. No.
Again, per the DMG, p141…
Many items, such as potions, bypass the casting of a spell and confer the spell’s effects.
The rule for concentration applies if the magic item allows you to cast a spell. It does not apply if the magic item grants you a spell-like effect. The stats on a Ring of Invisibility say
While wearing this ring, you can turn invisible as an action.
It does not say you can cast the spell Invisibility…just that you may turn Invisible as an action. This is an important distinction.
Thus, a Ring of Invisibility does NOT consume your concentration as it grants a spell-like effect, rather than allowing you to cast a spell. A Ring of Water Walking is another example of this, in that it allows you to walk on water at-will, rather than allowing you to cast the spell Water Walking.