No, it doesn't.
Sdjz's answer already makes a good argument, but I would like to add another conjecture:
If a spellcasting focus needed attunement, spellcasters using it would be in a large disadvantage, as you can only attune to 3 magic items at the same time. Obviously this implication is not enough to answer, but it should help to see that requiring attunement would lead to an awkward path.
An item can be attuned to only one creature at a time and a creature can be attuned to no more than three
magic items at a time.
Other than that, Attunement is a specific property and any item that has that property explicitly states it. The spellcasting focus does not. As an example, read the Druidic Focus
Druidic Focus. A druidic focus might be a sprig of
mistletoe or holly, a wand or scepter made of yew or
another special wood, a staff drawn whole out of a living
tree, or a totem object incorporating feathers, fur, bones,
and teeth from sacred animals. A druid can use such an
object as a spellcasting focus, as described in chapter 10.
Nowhere in the item it mentions anything about attunement, thus it does not require attunement. The same is true for every other (common/from PHB) spellcasting focus I'm aware of. In particular, the same is true for Holy Symbol and Arcane Focus.
As a final conjecture, an Arcane Focus (or any other spellcasting focus) is, mechanically, practically the same as a Component Pouch. I believe it's easy to see that requiring attunement to a Component Pouch makes little sense. From the first argument, if you require attunement to a Focus, you are just telling your players to use Component Pouches instead.