In France, there is an authority known as Académie Française, or in English, "French Academy". It is made of forty members, known as les immortels, or "the immortals". The Académie was founded in the 1600s to define the French language, and to eliminate the "impurities" of the language.
Today, they don't have any legal power (though they traditionally have the President of France as a patron), yet they are sufficiently respected that when they announced that the formal word for email was "courriel" (a portmanteau of the phrase "corrier electronique" or "electronic mail"), formal writing changed to reflect the decision.
However, casual speech does not always reflect the standardised French as defined by the Académie, and that speech can drift.
Let's imagine a language that is standardised, but is not used casually. There is actually such a language already in existence: Latin. Latin is a "dead language", in that there are no native Latin speakers, and no one actually knows how the Romans spoke it. It is, however, spoken by linguists who study Latin, students who learn Latin in school, and by scientists, since many scientific names are given in Latin.
If we discount the coining of new proper nouns and borrowing old ones from other languages as linguistic drift (I mean, when I say "My friend Xerses", you know I mean "Xerses" as a name, even if you've never heard the word before), then Latin rarely changes.
And I say "rarely", because it does change. When people make new inventions, some get new nouns and verbs associated with them. For example, a "car" in Latin would be a "currus automobilis" or "autocinetum", according to Wikipedia (Latin).
The only way to prevent the creation of new words by this route is if humanity ceased to innovate. Perhaps innovating is no longer enjoyable or economically viable. Perhaps there's nothing left to innovate. Either way, no new concepts means that humans will no longer seek to put new concepts into a language.
Combined with a practical reason to know a language but not use it casually (perhaps, as @Charlie Hersberger suggests, it is used to interface with (poorly programmed – they forgot
/internationali(s|z)ation/... sorry, regex joke) computers, or perhaps the language is used to cast magic), then Latin may actually become a language that has no linguistic drift.
Of course, if everyone gets an implant at the age of 5 that stimulates the brain in the right way to make them rapidly learn the "correct" way of speaking Latin, and gives a negative stimulus if they speak it incorrectly, that too would be sufficient.
And if a language is defined for its use in a specific role (for example, Aviation English), then it's possible that it is already static.
Many thanks to AlexP for a factual correction on the Latin translation for "car".