Spells with no components cannot be counterspelled
Counterspell says that it is cast as a reaction
which you take when you see a creature within 60 feet of you casting a spell
So a spell must be visibly being cast in order to qualify for counterspelling.
The components of a spell are what make the casting visible since a spell can have no effects (visible or otherwise) until its casting is complete. So removing those components completely will indeed make a spell's casting imperceptible.
This is confirmed by a section of optional guidance in Xanathar's Guide to Everything which says:
If the need for a spell’s components has been removed by a special ability, such as the sorcerer’s Subtle Spell feature or the Innate Spellcasting trait possessed by many creatures, the casting of the spell is imperceptible.
Thus, if using Subtle Spell on a spell would result in it having no components left as part of the casting, that casting would be immune to counterspell. Specifically this works for spells that have no material component. Spells with a material component would still be visible and counterspellable even after using Subtle Spell.
Rules as Intended seem to agree
Jeremy Crawford also unofficially agrees in a Tweet:
Subtle Spell is meant to protect a spell w/o material components from counterspell, since you can't see the casting.