A fire department official had said Abe appeared to be in a state of cardiac arrest when airlifted to hospital.
Police said a 41-year-old man suspected of carrying out the shooting had been arrested. NHK quoted the suspect, identified as Tetsuya Yamagami, as telling police he was dissatisfied with Abe and wanted to kill him.
Abe was making a campaign speech outside a train station when two shots rang out at about 11:30 a.m. (0230 GMT). Security officials were then seen tackling a man in a grey T-shirt and beige trousers.
"There was a loud bang and then smoke," businessman Makoto Ichikawa, who was at the scene, told Reuters, adding that the gun was the size of a television camera.
"The first shot, no one knew what was going on, but after the second shot, what looked like special police tackled him."
Earlier, Kyodo news service published a photograph of Abe lying face-up on the street by a guardrail, blood on his white shirt. People were crowded around him, one administering heart massage.
Nara emergency services said he had been wounded on the right side of his neck and left clavicle. His brother, Defence Minister Nobuo Kishi, had said Abe was getting blood transfusions.
NHK showed live footage of Abe's wife, Akie, on her way by train to the hospital where he was being treated.
Airo Hino, political science professor at Waseda University, said such a shooting was unprecedented in Japan. "There has never been anything like this," he said.