No, this isn't a design from SpaceX—but given Elon Musk's ambitions when it comes to interstellar travel, it wouldn't be surprising to learn he's got something like Charlie Automotive's CYBER6 v2 concept on the drawing board.
Charlie Automotive is a San Francisco-based industrial design outfit. This design was first posted on Instagram and captioned, "CYBER6 v2| What other versions can we imagine for the Cybertruck on the moon? Let me know!"
In Charlie Automotive's rendering the Cybertruck was used as the basis for an otherwise redesigned vehicle that really does look ready for the near-vacuum of the lunar surface. There's an additional axle and the wheels are made for otherworldly terrain—this concept Cybertruck looks like it could go pretty much anywhere.
The designer also added the requisite life support and communications array which would make this a perfect vehicle for traveling widely across the Moon's light side—which hasn't been as well-explored as you'd think, given how comparatively primitive such technology was when man was actually on the Moon over 40 years ago.