Your question could use some narrowing. In general, it is true that so-called postmodern studies and issues will have very little impact on the actual practice of the experimental "hard sciences."
However, this is not to say that science is immune from postmodern debates and concerns, far from it. And this goes deeper than the "science wars" of the 1980s and the likes of Feyerabend, Latour, or, by way of reaction, Sokal.
The impossibility of some purely "objective" scientific meta-narrative was perhaps most influentially argued by Kuhn, but it is already inherent in the theoretical turns of quantum theory and the Copenhagen view (god playing dice), or even earlier in the conflict between Boltzmann's use of statistic mechanics and the pure physicalism of Mach.
While these may not be viewed as "postmodern" ideas per se, they really do fall under the same theoretical environment. Likewise, the failure of logical positivism to secure a firm basis for "objectivity" and to purge all metaphysics from science is a major theme within the general "postmodern" drift, which is admittedly a poorly defined revival of skepticism.
Meanwhile, such debates are very much alive in the social sciences, where many critics identify ideological structures in sociology, economics, medicine,computer sciences, and even neurobiology. From research to application, scientific practices are deeply affected by military, racial, and corporate agendas.
Obviously, the good-faith practice of science strives to remove affect, biases, and interests from research, theory, and experiment. But which topics of research are selected to begin with and, more importantly, which get funded, will aways, even in the "hard sciences," be subject to ideological and metaphysical biases, agendas, or assumptions.
But perhaps the least recognized "postmodern" turn in science itself is driven simply by the global expansion of scientific programs, the increasing specialization of research fields, and the irreversible reliance on highly complex, super-computerized mathematics that are all making adequate peer-review and consensus increasingly problematic.
This means it is harder now to view science as a unified and coherent practice than it was even two generations ago. And I believe even among many scientists there is an increased awareness of the instability of scientific "texts" and "meta-narratives," though they probably wouldn't use those terms. Such issues do form the general tenor of what is loosely called "postmodernism."
This is hardly a complete or adequate response, but I do offer it as a rejoinder to some of the other views expressed above, which I believe are bit too hastily dismissive.