The actor is still in custody following the reported attack on his partner, in the wake of the two previous arrests, according to US website TMZ.
The star allegedly had an outstanding warrant for his arrest from a previous charge when he was picked up.
Edward hit headlines just two months ago when it emerged that he had been arrested for domestic violence after a public spat with his girlfriend at Los Angeles' LAX Airport on October 30.
The woman involved in the argument had visible marks on her arm and Edward's bail was set at $50,000.
On November 21, the day before Thanksgiving, the actor was arrested for a second time in under a month, accused of assaulting the same girlfriend.
The American History X star has recently been banned from spending time alone with his six-year-old son Ethan, after his ex-wife Rachael Bella obtained a court order.
The young child tested positive for cocaine after spending time in Edward's care earlier in the year, although it is still unclear how it got into his system.
Edward, who has undergone several stints in rehab, has been in and out of trouble with the law over the years.
The actor's colourful personal life includes being sued by an ex-girlfriend, 14 years his senior, for 'assault', and ex-wife Rachael Bella filing for divorce before hitting him with a restraining order.
Height of fame: Edward became a household name after his role in Terminator 2