The 26-year-old was being mentored by judge Paloma Faith in the contest and released a statement, saying she was "truly sorry" for letting her fans down.
"Two years ago I realised that I had a problem with drugs. I was using them to cope with various issues I was going through at the time. I thought they would help me, but they were making the situation worse," she said in a statement.
"I made the decision myself to seek treatment and checked into the Priory Clinic. It gave me strength and helped me face the world. It changed me for the better. But addiction is tough, and I am sorry to say that I have relapsed on a few occasions since I left."
The BBC also released an official statement reading, "Due to personal reasons which have only just come to light, The Voice producers, the BBC and Beth have agreed that she should withdraw.