It is very hard to prove someone did not say something.
The etymologist users at Wikiquote have declared this as misattributed.
It is impossible to rightfully govern the world without God and the Bible.
Wrongly attributed to George Washington; while he is known to have made some official statements of public piety, this was not one of them; it is sometimes wrongly cited as having been in various official statements, but the earliest attribution of the remark yet located is one which cites no sources in Upper Room Bulletin, Vol. 7, No. 3 (23 October 1920).
Note: Wikiquote isn't a very strong reference to support this. They do link to the 1920 quote, but that isn't proof that it isn't older.
Meanwhile, the Fake History blog tracks several different variants - e.g. an 1835 biographer who claimed Washington said:
It is impossible to govern the universe without the aid of a Supreme Being.
By 1867, that had transmorphed into:
It is impossible to govern the world without God
While this isn't hard proof that Washington did not say the exact phrase given, it is reasonable to accept that this is a different quote from Washington that has been corrupted in the re-tellings.