The earliest science fiction I recall set in a post-scarcity environment is "Star Trek: TNG". Granted, the socio-economic impact of replicators is not a focus of the series or the movies, replicators are more of background/world-building device ("Tea, Earl Grey, hot")
Even more important than the sheer existence of the Minds was their egalitarian disposition and relationship to their pan-human co-citizens, and interesting tangentials like the Minds' polite yet firm declination to Sublime. I will sorely miss Banks' weaving of the tales of the proto-Culture, and how the early Minds came about to that position.
Post-scarcity and post-singularity are orthogonal - The Culture is both, Star Trek TNG is post-scarcity only, Rapture of the Nerds[1] (Stross & Doctorow) is post-singularity only.
1. http://craphound.com/rotn/Cory_Doctorow_and_Charles_Stross_-...
Any movie treatment of The Culture runs the constant risk of only getting the glossing highlights reel version that Dune received, and I'd be concerned that the mechanics of the story setting, neat as they are, in a movie would get in the way of telling the real story of Banks' more interesting themes via his incisive commentary delivered by holding up The Culture mirror-like, comparing to our own civilization.