Wikipedia defines a constructed language, or conlang for short, as "a language whose phonology, grammar, and/or vocabulary have been consciously devised by an individual or group, instead of having evolved naturally." Some conlangs are devised for a culture in a work of fiction; others are intended as a worldwide second language.
SIL International maintains ISO 639-3, an international standard listing notable languages and giving each a 3-letter code. SIL defines a "full language" eligible for a code as one "used in a variety of domains, used to support communication across all genders and all ages, and stable enough to be widely understood across the whole area of the language." This is contrasted with a special-purpose language, such as an avoidance, ceremonial, or slang language. For example, Oddle Poddle from Flower Pot Men isn't as much a language as a dialect of Northern England English, and Ham-Chat is a set of slang terms used on top of English. A language for human communication can be registered and assigned a code if it has a literature and has been learned by multiple generations of speakers. Languages not in ISO 639-3 are not eligible for a new language edition of Wikipedia nor eligible to be included in Translatewiki, the project to translate interface messages in MediaWiki.
The same policy states that Wikimedia projects also cannot be established in "fictional languages", which I take to mean languages constructed to support a work of fiction under copyright, even if they have an ISO 639 code. This may represent an attempt to avoid legal threats like those by ViacomCBS against the Axanar team over Klingon and by the estate of J. R. R. Tolkien against type designer Dan Smith over tengwar. Sorry, conlangers: even if your language becomes the next Esperanto, it can't have a Wikipedia until 70 years after your death.
Articles about a language in Wikipedia are subject to a less rigorous notability standard. Under English Wikipedia's general notability guideline, any language that "has received significant coverage in reliable sources that are independent of the subject" is eligible for an article based on the information in those sources. Thus Wikipedia has an article about tlhIngan Hol, the language of space-faring Klingons in the TV series Star Trek, even if not articles written in that language. By contrast, Wikipedia lacks articles about many conlangs reviewed in jan Misali's web video series Conlang Critic because three independent scholarly or mainstream sources have not covered the languages.