No, Hubble is in low Earth orbit, much lower than the Moon. The shuttle delivered it to orbit, and the Shuttle can't get near the Moon.
The image you reference is very similar to one that came from DSCOVR, which is at a point about a million miles from Earth between the Earth and Sun, which always sees the sunlit portion of the Earth. However, there are some differences that just don't quite make sense. It seems more likely that someone simply inserted a picture of the Moon over the Earth. One of the key ways you can tell this is that the Moon is brighter than Earth, while in reality, the moon is rather dark. In fact, the brightness of the Earth and Moon should be reversed, the Earth bright, and the Moon dim.