Both of your examples are uses of parenthetical phrases and they're both technically fine. There are some slight problems with the usage but I'll address that below.
A parenthetical phrase, sometimes called simply a parenthetical, is one that is not essential to the framing sentence. In the preceding sentence, the phrase “sometimes called simply a parenthetical” is itself a parenthetical because the segments of the sentence that precede and follow it can be attached to form a complete sentence without it: “A parenthetical phrase is one that is not essential to the framing sentence.”
What this doesn't say is that, often, these unnecessary phrases are set apart with commas.
So, while you lose some information by excluding "not intrinsic", the sentence is complete without it.
As the other answer indicates, the first sentence feels a bit incomplete.
You actually have at least two options to remove this lack of specificity.
First, you can do what user3169 recommended and add some framing to "intrinsic":
It's an acquired habit, not an intrinsic one.
The other option is to keep the sentence ending the same but make "habit" the subject:
The habit is acquired, not intrinsic.
Because habit is the subject, rather than "it", there's no need to explain what "intrinsic" relates to.
The second sentence is perfectly fine as it is. Because you've placed "not intrinsic" between "acquired" and "habit", it's not necessary to include "habit" with "intrinsic" in this version.
It's an acquired, not intrinsic, habit. (good)
*It's an acquired, not an intrinsic habit, habit. (weird)