It wouldn't lead to hyperinflation as hyperinflation implies that the money actually still holds some sort of tangible value, albeit incredibly low. Instead we'd see a global economic shutdown overnight. People would simply stop working, period.
See, the problem is that replicators would have to be produced in quantity and be immediately available to the entire human populace. Otherwise people still have to be employed, to get the replicators distributed, but who would willingly do that for no pay if money is no longer worth anything because all known sources of wealth can be conjured up at the push of a button?
Of all the takes on how to introduce seemingly "magical" technologies to a human populace woefully unprepared for them, I think Stargate has the right idea: little bits at a time doled out by the government to private enterprises to reverse-engineer and market as a means of slowly transitioning the populace from a labor-based economy to an ideas-based economy. If production of material goods is entirely automated, all that's left for us to do is to design things to be produced (and used), which incidentally is one thing Star Trek got right with human society's focus appearing entirely concentrated on service in (or supporting) StarFleet, the Federation StarFleet being far more than simply a space navy, but that plus a coast guard and public works organization all wrapped into one.
