Mathematics is language pushed to the limits of objectivity and precision, where all concepts are clearly defined and interrelated, and their articulations are governed by explicit rules. In that context Gödel's theorem states a fundamental incompletude of language itself. 

As long as we define physics by what we know about the world, it is submitted to the same limitation: language will never be complete enough to describe the world, because language in its very essence is intrinsically limited.

Now physics is more than the elaboration of a description of reality: it is an actual interaction with reality, at more and more subtle and deep levels. There is no indication of a hard limit to that endeavour.