I suspect you don't but I'm not sure. In the description of opportunity attacks:
You can make an opportunity attack when a hostile creature that you can see moves out of your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature. The attack interrupts the provoking creature's movement, occurring right before the creature leaves your reach.
You can avoid provoking an opportunity attack by taking the Disengage action. You also don't provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction. For example, you don't provoke an opportunity attack if an explosion hurls you out of a foe's reach or if gravity causes you to fall past an enemy.
Teleports are explicity excluded from opportunity attacks, however I'm not sure that Etherealness (either the ability or the spell) is a teleport. For example the Night Hag's ability:
Etherealness. The hag magically enters the Ethereal Plane from the Material Plane, or vice versa. To do so, the hag must have a heartstone in her possession.
The Etherealness spell a bit more descriptive:
You step into the border regions of the Ethereal Plane, in the area where it overlaps with your current plane. You remain in the Border Ethereal for the duration or until you use your action to dismiss the spell. During this time, you can move in any direction. If you move up or down, every foot of movement costs an extra foot. You can see and hear the plane you originated from, but everything there looks gray, and you can't see anything more than 60 feet away.
While on the Ethereal Plane, you can only affect and be affected by other creatures on that plane. Creatures that aren't on the Ethereal Plane can't perceive you and can't interact with you, unless a special ability or magic has given them the ability to do so.
You ignore all objects and effects that aren't on the Ethereal Plane, allowing you to move through objects you perceive on the plane you originated from.
When the spell ends, you immediately return to the plane you originated from in the spot you currently occupy. If you occupy the same spot as a solid object or creature when this happens, you are immediately shunted to the nearest unoccupied space that you can occupy and take force damage equal to twice the number of feet you are moved.
This spell has no effect if you cast it while you are on the Ethereal Plane or a plane that doesn't border it, such as one of the Outer Planes.
It is not clear to me if it is a movement, a teleport, both or neither. So the first question if it is a teleport or not? If yes, then it's easy, no opportunity attacks. However it doesn't say "teleport" or "transport" as in other teleport spells like Teleport, Plane shift or Misty step
If it's not a teleport, the next question is whether it counts as moving, because you only get opportunity attacks if the enemy "moves" out of your reach. The ability and the spell says "enters" and "step into" respectively, so it might qualifies as moving.
The next problem is whether it moves "out" of your reach or not, since it basically remains on the same spot, just on a different plane.
My confusion probably comes from not understanding the Ethereal plane well.