For pretty much any grammatical category, I can think of a language in which it's a closed class. Japanese has closed classes of verbs and (verb-like) adjectives, for example, while Swahili has a closed class of (noun-like) adjectives.
However, I can't think of any instance of the class of nouns being closed. It makes intuitive sense for this to be a universal, since giving names to objects is a pretty fundamental part of human language use. But it's equally possible that I just haven't looked at enough languages to find a counterexample.
So: is there any natural, attested language in which nouns are a closed class?
P.S. By "closed class" I mean a class that resists adding new members, like English pronouns—compare the backlash against singular "they", which has been used since before Shakespeare, to the immediate acceptance of the new verb "to google".