It might hang from a wall, but I agree hang on is odd when talking about a shelf.
For those who don't know: if something is flat against a wall (or chimney or similar), it hangs on (or against) the wall, but if it not flat against the wall and it proportionally sticks out, it generally hangs from the wall.
A single shelf hanging from a wall is still somewhat odd. A single shelf simply wouldn't be stable if hanging. A single shelf is normally mounted on a wall, as jairapetyan suggests.
A set of shelves could be hung on a wall though, like this, because the structure of the shelves would prevent a single shelf from falling over. If hyllan in this case is referring to a set of shelves, and the English translation is adjusted to "the shelves hang on the wall", it would also make sense.
I would change the English to "The shelf is mounted on the wall".
In my upbringing, if something is hung on a wall, it should be against the wall, not necessarily flat against it. Perhaps it's regional? I'm from Vancouver, Canada, with a British mother long naturalised and a Canadian father. We (my family/friends) wouldn't say that a shelf hangs from a wall unless there's a space between the object and the wall, as something hanging from a hook that sticks out. Though in that case we'd also be inclined to be more precise and say "hanging from a hook in/on the wall". In speaking of a wall-hung shelf, I would automatically say "hangs on the wall". Perhaps it's partly in the meaning of the word hang, which has several correct definitions, such as 1.1 and 1.2 in the Oxford English dictionary: http://www.oxforddictionaries.com/definition/english/hang
Actually "hang on" is better. "Hang from" implies that it's loose, so favoring "from" refers to an exceptional situation. It is possible to hang a shelf on the wall if it is fastened with hooks. I have a knick-knack shelf hanging on my kitchen wall. No way would I want it hanging from the wall like those dangling bottles in a song that some one else here mentioned.
I concur with photodiarist and pekarekr. I came to this thread because “hangs from the wall” sounds distinctly wrong to me. To “hang from” something, an object would need to be dangling away from its stated support. An object can hang from a ceiling, or even from a hook on a wall, but not from a vertical surface itself; a thing can jut out away from a wall, but not hang from it. The phrasing has to follow our sense of gravity.
There is absolutely nothing wrong, on the other hand, with “the shelf hangs on the wall.” If something appears to hug the wall, it can be said to be “on the wall”. Contrary to "hanging from", the hanging aspect here does not indicate dangling; it merely expresses that the object does not extend all the way down to the floor and gets its support instead from the wall. “Hanging on the wall” means attached to the wall by whatever means, and not limited to one point of support. I imagine “hänger på väggen” carries the same idea.
I've honestly given up on trying to make this sentence idiomatic in English. If you look up, you'll see that e.g. Mark the Muppet and jairapetyan both dislike "on", and they're native English speakers whose judgement I trust as much as I do yours.
I can't remember if I did frequency counts the last time I revised this sentence. To be clear, both "on" and "from" are accepted, but I don't think I'll even find a single version I can use to please everybody.
Not to beat a dead horse, I would like just to add the observation that those who take exception to "hangs on the wall" do so out of a too-narrow interpretation of the verb "hang" -- that a hanging item must take a single point of support from above and therefore its stability would be in question in the case of a hanging shelf. The definitions that aptly apply to this sentence, though, are listed in the 1971 edition of the Oxford English Dictionary as #12 -- "To remain suspended without visible support" and #14-b -- "To attach oneself for support. Of things: to stick, adhere, cleave". For comparison, OED gives this citation from Tyndall's Glacier (1860): "Secondary glaciers ... hanging on steep slopes." Take a look here at such a sight -- https://www.usgs.gov/centers/norock/science/secondary-glacier-network?qt-science_center_objects=0#qt-science_center_objects.