'The avenue is closed off' is a more natural translation of this, which I didn't use lest it be dinged.
Firstly: as someone who spent a few years growing up in North America, the word 'avenue' is completely disconnected in my mind from tree-lined streets, which is what שדרה is. I would personally use boulevard for שדרה instead. Besides, the older שדרות in Israel like Rothschild in Tel Aviv are much more like European boulevards than European avenues.
Boulevard is שדרה and boulevards is שדרות (Sderot, like the city). In that sense you can also say that avenues is שדרות.
However, an avenue can also be "a means of access or attainment" or "a way or means of entering into or approaching a place" (Dictionary.com). These meanings are translated as אפיק in Hebrew, and the plural is אפיקים.
In AE, saying that"the avenue is closed" can have two different meanings; one that the road itself is closed to traffic, and another that all the stores in a shopping district along a main street have already closed. Does anyone know if "השידרה סגורה" can also have either meaning in Hebrew?