Almost certainly not.
But that's not much fun, so let's try and think of ways to make it even remotely plausible:
First, the creature could use an actual moon or large asteroid as a core; i.e. the biological portion is only a relatively thin (though still stupendously massive) layer on top. This would dramatically cut down on the energy required to reproduce, and give it a structural core that it didn't need to grow itself.
The host planetoid could be the source of most the raw materials for the actual creature. It could also serve as a giant heat sink/source to help stabilize its temperature. The creature could dump heat into its core when energy is plentiful (when near a star, or feeding,) and draw upon it when it's scarce (i.e. in deep space.)
How it moves is going to be a problem. Barring science fiction Warps and such, the only remotely plausible (still nuts, note) method I can think of is something like a planetary-scale ion drive, where it continuously accelerates and ejects a small amount of core mass at extremely high velocity. Very little thrust, but excellent efficiency. It would also take advantage of gravitational slingshots as much as it can (being intelligent would be very helpful here.)
All of this means that the sucker is going to be very slow. You can model it pretty well from the more realistic generational space ship ideas. Hundreds if not thousands of years between target systems, during which it will need to be in a basically-dead hibernation state ("In his house at R'lyeh dead Cthulhu waits dreaming...")
Then of course there's the issue of how & why it feeds on intelligent species... In any realistic scenario it would be much easier and filling to just feed on stellar radiation. You'd pretty much have to have a "psychic energy" angle in your world to make it plausible. Which given the Lovecraftian nature of the critter you may well have anyway.