I'm going to go out on a limb here: Yes, it is limited to this universe.
There is no direct canonical evidence for this, but a great deal of indirect evidence.
As I bring these examples up, please bear in mind that (various poorly-written episodes notwithstanding) Starfleet personnel are normally expected to give their lives to uphold the Prime Directive. What we see, time and time again, is the exact opposite of this. Decorated officers completely ignore the Prime Directive, usually to save their own lives, and not only are they not punished, the PD isn't even brought up as an issue, then or later.
First, consider "Mirror, Mirror" (TOS) (we're skipping ENT because the Prime Directive was not yet in force at that time). Kirk quite deliberately alters the course of history in the mirror universe. What's more, he does so by persuading mirror!Spock to completely change the fundamental principles of the Terran Empire. I should also note that Kirk describes the mirror universe as "savage," and Spock calls its inhabitants "uncivilized." Since the Prime Directive seems to apply especially strongly to less advanced races ("First Contact", TNG, and many other episodes), this is quite telling.
Jump ahead to "Crossover" (DS9). Kira and O'Brien participate in a small-scale rebellion within the mirror universe. This rebellion is strongly implied to have ultimately succeeded, at least at the local level. Again, they changed the course of history in a drastic fashion.
When Picard suggested intervening in the Klingon Civil War, Fleet Admiral Shanthi initially rebuffed him, until he argued that the Romulan Star Empire was likely involved as well ("Redemption II", TNG). This suggests the Prime Directive specifically forbids becoming involved in somebody else's purely internal rebellion or civil war, even if the "somebody else" is (at the time) a close ally of the Federation.
Later, in "Through the Looking Glass" (DS9), Sisko further aids that same rebellion, impersonating its leader (his late mirror self) and persuading mirror!Jennifer to join the rebellion. In "Shattered Mirror", he assists in the repairs of the mirror!Defiant, and even captains it briefly, all to support the rebellion.
I can't find any clear PD violations in (Memory Alpha's summary of) "Resurrection" (DS9).
While DS9 has a few other examples of characters interacting with the mirror universe, the most blatant violations (in "The Emperor's New Cloak") were not carried out by Starfleet personnel, so I can't really fault them here.
So far as I'm aware, at no point in any of the live action shows or movies does anyone bring up the Prime Directive in relation to any parallel universe. The silence here is deafening. On numerous occasions, parallel universes are altered to suit the needs of our main characters, and at no point is this regarded as violating the PD. In DS9's "Playing God" (props to @Keen for catching this), ethical issues are brought up, but the PD is not. At some point, we have to draw the obvious conclusion: The Prime Directive is never mentioned because it does not apply.