Bale, 34, is alleged to have lashed out at the two family members in his suite at Park Lane's Dorchester Hotel on Sunday.
The British actor, who plays the Caped Crusader, is being questioned at a central London police station, sources added.
The two women, who live in Dorset, went to a Hampshire police station yesterday
to make a formal allegation.
The complaint about the actor was then passed to the Metropolitan Police for
further investigation.
A police spokeswoman said: "A 34-year-old man attended a central London police station this morning by appointment.
"He was arrested in connection with an allegation of assault. He currently remains in custody."