No. Dispel magic affects spells, and a beholder's eye rays are not spells. Nor can you dispel antimagic field or shell or whatever it's called in 5e, as far as I recall.
Creature abilities that are not spells can't be dispelled.
If the ability replicates a spell effect... well, that would normally be an interesting question: Does it replicate it to the extent of being dispellable? In this case, however, the question is moot. Antimagic field isn't dispellable even when you actually do cast it as a spell, so it certainly isn't dispellable coming from a beholder.