High Court justice Michael Tugendhat says Hong has been hounded outside her London home and feels that "her life has become unbearable."
He has granted an injunction "prohibiting harassment" of the actress and her daughter.
The injunction was granted last week, and Tugendhat outlined his reasons on Friday.
Grant's spokeswoman confirmed earlier this month that the actor had recently fathered a child after a brief fling, and he and Hong remain on good terms.
The judge said Grant and Hong "did their best to keep private" the fact that they had a child, "and do not know how the information reached the public domain."