Can Shannon's entropy be used to determine if a file is encrypted? If we have to determine a file is encrypted or not, can we use Shannon's entropy algorithm on the file? 

As discussed here, the entropy (in bits per byte) being closer to 0 is considered as more orderly and being closer to 8 is considered more random. 

Intuitively this might be generating false positives a lot. Can any one explain if this approach is appropriate to determine given a random file is encrypted or not?
You are likely going to have both false positives and false negatives if you try to use Shannon entropy for this.


Many compressed files would have close to 8 bits of entropy per byte, resulting in false positives.
Any encrypted file that has some non-binary encoding (like a file containing an ASCII-armored PGP message, or just a low entropy header) could have a lower entropy, resulting in false negatives.
If Format Preserving Encryption is used , this might result in false negatives too


It may work as a heuristic, but you should not rely on the results being correct.