The 21-year-old Carroll was arrested in October and ordered by a court to live in the family home of Newcastle team-mate Kevin Nolan following an allegation he assaulted an ex-girlfriend.
The CPS, a government department responsible for prosecuting those charged with an offense, says it isn't proceeding with the case against Carroll because there is "no longer a realistic prospect of conviction."
Carroll is the joint-second leading scorer in the Premiership this season with 10 goals. He made his England debut last month in a friendly against France at Wembley.