The incident, which took place in February in New Jersey, caused the Ravens to suspend Rice in July for two games for breaching their policy on personal conduct.
However, the franchise have now opted to cut ties with the player indefinitely after the CCTV footage came to light via the American website.
A statement from the White House said: "The President is the father of two daughters. And like any American he believes that domestic violence is contemptible and unacceptable in any civilised society.
"Hitting a woman is not something a real man does, and that's true whether or not an act of violence happens in the public eye, or, all too often, behind closed doors.
"Stopping domestic violence is something that's bigger than football, and all of us have a responsibility to put a stop to it."
The couple have since married following the incident.