Shannon information (entropy, actually) is an abstract concept that applies first and foremost to strings over an alphabet of symbols. In that sense, it is nonphysical (I would prefer to call it abstract, in the sense of abstracting from the real world onto simpler models of the world).
Curiously, it turns out that defining entropy still makes sense more generally in statistical mechanics and it looks pretty much the same as Shannon entropy. Read more on Wikipedia. This has implications about the physicality of information (even abstract information). Since any abstract information needs to be represented physically, it turns out, for example, that erasing (abstract) information from a physical medium takes a minimum amount of energy to perform. (Landauer's principle)
This is important, because it means you can do things like argue about algorithms (in particular cryptographical ones where entropy matters) in terms of minimum energy expenditure instead of runtime (or abstract complexity), and arrive at things like:
As a starting point, we will consider that each elementary operation
implies a minimal expense of energy; Landauer's principle sets that
limit at 0.0178 eV, which is 2.85×10^-21 J. On the other hand, the
total mass of the Solar system, if converted in its entirety to
energy, would yield about 1.8×10^47 J (actually that's what you would
get from the mass of the Sun, according to this page, but the Sun
takes the Lion's share of the total mass of the Solar system). This
implies a hard limit of about 6.32×10^68 elementary computations, which
is about 2^225.2. (I think this computation was already presented by
Schneier in "Applied Cryptography".)
The whole answer is worth a read and the comments, too.
I think that makes information pretty physical, even if the original definition by Shannon is abstract.