The zoo said it was “thrilled” with Zaiya’s “rare” birth.
The indoor elephant enclosure was closed to the public for nearly a month while the herd developed “crucial bonds” with the calf.
Zaiya was the first successful female elephant birth at the zoo.
The zoo’s director Darren Webster said it was a “truly historic moment”.
He added: “This achievement further reinforces our dedication to the conservation of all endangered species and I could not be prouder of our team.”
Asian elephants have been listed as endangered since 1986, with populations estimated to have declined by at least 50% over the last three generations.