More specifically, I am speaking of formal (official) style texts. Definitely not belles-lettres or informal speech. We know, in formal style texts, such as documents, abbreviations are frequently used. But may you ever abbreviate the word ноябрь (or any of its case forms), which is the Russian equivalent of November?
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 months' abbreviations 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 so far I haven't seen any official document prescribing this particular form (which by the way does not necessarily mean that such a document does not exist). Still, as I mentioned in my comment - you can see them fairly often and people usually don't even notice that the months' names are abbreviated, which means they look perfectly natural for a Russian eye.
Update Well, V.V. gave 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 the needs of English, does not 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.
Therefore, 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 year November: https://ru.stackoverflow.com/search?q=date%3A2019-11
Change the search query to see the results for other month names.
This is just an example, not an official style guide. But the community there takes pride in perfecting the Russian translations and designations; they have posted more than 700 bugs already.