A spokeswoman said there were no complications from the procedure, performed at Emory University Hospital in Atlanta, for a subdural haematoma, or blood on the brain surface.
Mr Carter, 95, will remain in hospital for observation, said Deanna Congileo, his spokeswoman at the Carter Centre.
The statement said the Carters thank everyone for the many well-wishes they have received, and Ms Congileo does not anticipate making more announcements until he is released.
It was unclear how long he might be in hospital, said his pastor, Rev Tony Lowden.
"If anybody can make it through this, Jimmy Carter can. His will to serve is greater than his will to give up," said Rev Lowden.
The Carter Centre said the bleeding was related to Mr Carter's recent falls. He used a walking frame during his most recent public appearance.
The first fall, in the spring, required hip replacement surgery. He hit his head falling again on 6th October and received 14 stitches, but still travelled to Nashville, Tennessee, to help build a Habitat for Humanity home shortly thereafter.
He was briefly treated in hospital after fracturing his pelvis on 21st October.
Mr Carter's wife of 73 years, Rosalynn Carter, is with him at the hospital, Rev Lowden said. "She won't leave his side," he added.
The former president has been through a series of health problems in recent years.
He received a dire cancer diagnosis in 2015, announcing that melanoma had spread. After partial removal of his liver, treatment for brain lesions, radiation and immunotherapy, he said he was cancer-free.
Despite increasingly frail health, the nation's oldest-ever ex-president still teaches Sunday school about twice monthly at Maranatha Baptist Church in his home town of Plains, Georgia.
The church said he will not be teaching his Sunday school class this week.
Mr Carter candidly discussed his own mortality on 3rd November, during his most recent appearance at their church. Referring to his cancer diagnosis, he said he assumed he would die quickly after finding out the extent of his illness.
"Obviously I prayed about it. I didn't ask God to let me live, but I just asked God to give me a proper attitude toward death. And I found that I was absolutely and completely at ease with death," he said.
Since then, Mr Carter said he has been "absolutely confident" in the Christian idea of life after death, and has not worried about his own death.
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