The zookeepers named her Hope to "symbolise a ray of light and hope at a time which felt so bleak".
The zoo's managing director Larry Bush said they were "devastated", saying she was "full of energy and life and she was a very healthy young zebra".
"It's such a tragedy that she has lost her life, seemingly as a result of fireworks being set off at nearby events which were intended as a celebration."
And senior keeper Jayne Gibbins said her birth was a "real high point amongst the challenges of having to close the zoo for three months in support of the national lockdown and we are all feeling her loss greatly".
The zoo hopes her death becomes an "impetus for change' to raise awareness about the impact firework displays can have on animals.
Bush added: "We know this was not the intention of local organisers and people letting off fireworks but it does demonstrate in a tragic way the impact that fireworks can have on animals whether this be zebras, horses, native wildlife or pets in our homes."