The conjuration wizard school has an ability named Focused Conjuration which says
Beginning at 10th level, while you are concentrating on a conjuration spell, your concentration can’t be broken as a result of taking damage.
The elder brain has the legendary action Break Concentration which says
The elder brain targets a creature within 120 feet of it with which it has a psychic link. The elder brain breaks the creature's concentration on a spell it has cast. The creature also takes 1d4 psychic damage per level of the spell.
So if a wizard has the spell conjure elemental up and the elder brain uses its Legendary Action, is the wizard's concentration broken?