Carter's lawyer argued she should remain out of jail while they appeal her case to the US Supreme Court.
Daniel Marx, who argued the case before the Supreme Judicial Court, said last week that the court's ruling "stretches the law to assign blame for a tragedy that was not a crime".
A MA judge on Monday ordered Michelle Carter to start serving her sentence for persuading her boyfriend to kill himself in 2014.
The juvenile court judge focused his guilty verdict on the fact that Carter told Mr Roy over the phone to take actions which led to his death. She has remained free as she appealed her conviction, which was upheld in Massachusetts Supreme Judicial Court last week. Carter had also been treated for anorexia, and Roy had made earlier suicide attempts.
Last week, the judge said Carter, now 22, had a duty to call the police or Roy's family when she knew the 18-year-old meant to kill himself. Their relationship consisted mainly of texting and other electronic communications.
The case received global attention and provided a disturbing look at teenage depression and suicide.
"I thought you wanted to do this". No more pain. It's okay to be scared and it's normal.
Prosecutors had argued Carter could have stopped Roy from killing himself, but instead bullied him into going through with his plan through text messages that became more insistent as he delayed.
"As the defendant herself explained, and we repeat due to its importance, '[The victim's] death is my fault like honestly I could have stopped him I was on the phone with him and he got out of the [truck] because it was working and he got scared and I f-king told him to get back in, '" the court wrote in its decision.
In dozens of text messages revealed during her sensational trial, Carter pushed Roy to end his life and chastised him when he hesitated.
The DA broke the news in a tweet at 12:48 p.m. on Monday, just under two hours before a Taunton Trail Court judge was scheduled to rule on the motion. Her attorney said Roy was determined to kill himself and nothing Carter did could change that.
"The Roy family is glad to have this aspect of the case over", the family's attorney, Eric S. Goldman, said in a statement. The justices said Carter preyed upon Roy's "well-known weaknesses, fears, anxieties and promises" and overcame the "mentally ill, vulnerable" young man's will to live.