The only mention about the usage of this symbol in Russian on the English Wikipedia page says this:
Although the letter "N" is not in the Cyrillic alphabet, the numero sign is typeset in Russian publishing, and is available on Russian computer and typewriter keyboards.
However, according to the Russian version of the page (ru.wikipedia.org/wiki/Знак_номера), this was borrowed from the French sometime during the 19th century. Here's the exact quote from Wikipedia:
Во французской типографике в XIX веке обозначался как № (и был в таком виде заимствован в Россию); сейчас принято обозначение N o, n o (N os и n os для множественного числа) или No.
Incidentally, this appears to have fallen out of favor in contemporary French.
The numero symbol is not in common use in France and does not appear on a standard AZERTY keyboard. Instead, the French Imprimerie nationale recommends the use of the form "no" (an "n" followed by a superscript lowercase "o"). The plural form "nos" can also be used.