According to several sites, the first duty-free shop opened at Shannon Airport in Ireland in 1947, since when duty-free shopping has become an enormous international business even though some airlines have discontinued sales on flights.
Finding references to duty-free shops on passenger ships has proved much more difficult, though. According to these (un-referenced) Quora posts, there was no duty-free shop on the Titanic (but one of the answers gets the date and place of the first duty-free shop wrong).
The only other information I have is from childhood: I remember duty-free shops on the DFDS ships MS Winston Churchill and MS England on the Harwich (England) - Esbjerg (Denmark) route in the early 1970s. While I was plundering the liquorice supplies, my parents were stocking up on more 'standard' duty-free items (alcohol, cigars / cigarettes, perfume). MS England's last round trip on this route was in July 1974, but I can't say how long before that there was a duty-free shop.
This article, 70 years of achievement in duty free and travel retail, provides some interesting background information about duty-free sales before the jet age, stating that
personal hygiene requirements in the crowded space of a small ship or horse-drawn coach were probably the origin of today’s allowances for perfume. But even when duty free sales started to become more formal, the progress from “sustenance” towards the idea of “personal export” was a slow one.
To clarify, I'm not interested in diplomatic or military special privileges mentioned in the article above, but in duty-free shops for ordinary people looking for some of the aforementioned "personal export" while en route from one country to another.
In anticipation that the line between "sustenance" and "personal export" might be a little blurred, information on the former would also be of interest.