It is probably not a creature.
The term "creature" is not explicitly defined in 5e, so we have to look to other spells and situations for analogous situations.
Spells such as Unseen Servant and Bigby's Hand create entities that have some of the properties of creatures, like HP, AC, and grappling. Likewise, while the hound can make attacks, it doesn't have other game statistics like ability scores.
On the other hand, the spell Simulacrum explicitly states that its creation is a creature:
The duplicate is a creature, partially real and formed from ice or snow, and it can take actions and otherwise be affected as a normal creature.
Mordenkainen's faithful hound does not have such text, and neither do Unseen Servant or Bigby's hand. Thus, the hound is probably more like a magical object, similar to Mordenkainen's Sword.