I'm referring more specifically to formal (official) texts — definitely not belles-lettres or informal speech. We know that abbreviations are frequently used in formal texts such as documents, but is it ever possible to abbreviate the word ноябрь November (or any of its declined forms)?
There are official abbreviations in the dictionary Русский орфографический словарь: около 180 000 слов / Российская академия наук. Институт русского языка им. В. В. Виноградова / О.Е. Иванова, В.В. Лопатин (отв. ред.), И.В. Нечаева, Л.К. Чельцова. - 2-е изд., испр. и доп. - Москва, 2004. in the supplementary part "Основные общепринятые графические сокращения"
янв., февр., апр., авг., сент., окт., нояб., дек.
Some months don't have abbreviations: март, май, июнь, июль.
The answer to the question in the title is - yes.
A few examples of abbreviated months in Russian:
See also: http://tetran.ru/SiteContent/Details/13:
One could argue, however, that they can hardly be called "official" (as the body of the question clarifies) and I would agree with this because I've yet to see any official document prescribing this particular form (which, by the way, doesn't necessarily mean that such a document doesn't exist). Still, as I mentioned in my comment, you come across abbreviations for the months of the year fairly often and people usually don't even notice them. In other words, they look perfectly natural to the Russian eye.
Update V.V. provided an answer with a reference while I was busy typing the above.
In theory, the correct abbreviated form is the one given in V. V.’s answer. In practice, commonly-used software, typically tailored for English, doesn’t generate abbreviations of this kind. For example, MS Excel only has five options for formatting dates (9, 09, S, Sep, September)—notice how “Sept.” isn’t among these, even though Associated Press style prescribes exactly that.
Consequently, jarring Anglicisms such as “31 июн 2038” are commonplace because of software limitations. Even Yandex displays dates like that in its mail UI.
Stack Overflow на русском abbreviates it as 'ноя', which can be seen e.g. if you search for posts from last November: https://ru.stackoverflow.com/search?q=date%3A2019-11
Change the search query to see the results for other months.
This is just an example, not an official style guide. But the community there takes pride in perfecting the Russian translations and designations; they've posted more than 700 bugs already.