According to centre staff, the elephant named Yinen has been living in the centre for about nine years.
Last April, she naturally mated with a male elephant in the centre.
Yinen had a half-hour labour before giving birth to the calf following a 19-month pregnancy.
The female calf weighs 96-kg and is 91-cm tall, said Bao Mingwei, an official at the centre.
Bao said the baby elephant was able to stand on its own within minutes of the delivery, and was named Dongzhi, the Chinese term for "winter solstice," the day she was born, state-run Xinhua news agency reported.
Since its establishment in 2008, the centre has rescued 12 wild Asian elephants, nine of which are still receiving medical care in the centre.
The centre has delivered five calves so far.