Doctors in Atlanta have told the 91-year-old the tumours in his brain are being treated successfully and there are no signs of further cancer growth.
However, the spokeswoman said that doctors will continue tests.
Mr Carter, who served as president of the US from 1977 to 1981 and won a Nobel Peace Prize in 2002, announced his illness in August.
He said then he would receive radiation and chemotherapy for four tumours that had formed in his brain.
Media reports have suggested that Mr Carter was not experiencing any pain or discomfort during the treatments, and that his work with The Carter Center had not been scaled back.
The former president had been planning to travel to Nepal this month for volunteer work, but the trip was cancelled due to "civil unrest" in the country.
Former US President Jimmy Carter is responding well to cancer treatment, according to his spokeswoman.