Neither side would probably like to admit it, but there are more commonalities between Austrian economics and the postmodern perspective (there are many different flavors of post-modernism as well as Austrian economics, but I'm talking about elements common to most of them) than most people realize.
1. Ideology and Knowledge. Postmodernists argue that there is no neutral position to judge competing claims from; the location of the speaker is always bound up in his/her opinion. Austrians make the same point when criticizing "mainstream" economics, or defending Austrians against claims of being "overly ideological". See this video of a talk by Prof. Pete Boettke, and then click to the "Understanding the status quo of the Austrian School of Economics" section, and his arguments are not too different from what you'd hear from a cultural criticism Ph.D, although the tone and substance is very different.
2. Identity. Postmodernists emphasize the fragmented nature of human experience. Humans can't be seen as perfectly rational actors, or driven exclusively by moral principles... there are always competing claims for our attention. This is close to the subjectivist view of many Austrians, who argue that we can't know exactly why people act.
Unlike mainstream economics, which is sometimes willing to call behavior "irrational" if it does not seem to effectively address a goal, Austrians are more open to differing forms of rationality (to paraphrase, if you are acting by definition you wish to change the status quo, which means your act is rational being it is a means seeking an end). Austrians don't impose an overarching standard of rationality onto human behavior, which is not too far from a postmodern interpretation.
3. Information in Society. Austrians (particularly those drawing from F.A. Hayek) describe how information is diffused throughout society, and is not always available to a central planner. Also, institutions may emerge spontaneously from cooperation between people, without ever being explicitly planned by anyone. This isn't far from Foucault's view of social restraint or "biopower". The informal norms which guide us to believe some acts are acceptable and others are not spring from collective understandings of what is normal and what isn't. These norms can't be dictated from above, although government may be able to twist collective understandings to suit certain purposes. The language is much different, but this Foucauldian view is in line with the Austrians on many levels.
Of course, there are also many differences - postmodernists are skeptical of deductive logic which Austrians rely on heavily, and would probably describe such efforts as "essentializing" or "reductionism". Austrians dislike the postmodern openness to "sloppy" (non-deductive) argumentation, and excess optimism when evaluating government policy.
I'd argue that the intellectual tropes which postmodernists have helped build into common academic discourse have been seized and re-appropriated by Austrians toward their own goals (although perhaps unintentionally). In that respect, if the Austrians win in influencing policy it will be proving how postmodern our social viewpoint has become. Almost ironic.