The pregnancy could be a case of parthenogenesis - or asexual reproduction - which, although common in some amphibians, has never been reported before in sharks.
More likely, say the zoo's scientists, the shark was impregnated before she came to the center and retained a male's sperm in her reproductive tract until she was mature enough to conceive. However, researchers concede that even this explanation takes some believing.
Dogs and sharks
One idea being investigated is that the female bonnethead mated with a male leopard shark, which does share the same tank.
However, coupling between two different species is very rare and these two sharks are completely different sizes.
The director of zoo, Dr Lee Simmons, said mating between a bonnethead and a leopard shark would, in dog terms, be like a Chihuahua impregnating a Saint Bernard, and seemed most unlikely.
"The option, which is probably the most logical," he told the BBC, "would be that the animal was inseminated as an infant, almost a newborn, carried living sperm cells - viable sperm cells - in the reproductive tract for nearly three years until it was old enough to then become pregnant."
'Weird' case
Dr Simmons said this would still "rewrite the rules of reproduction as we knew them". "That would be extraordinary," he said.
DNA tests were begun this week on tissue and blood samples taken from the three-year-old female bonnetheads and the pup, which died five hours after it was born on 14 December after being bitten by a stingray that lives in the same tank.
Though sperm can survive inside a shark's reproductive tract for months or even years, asexual reproduction is unheard of in sharks, Simmons said.
"We want to know if there was a father or if there was a weird hybridization of species. It will make a damn interesting research paper," Dr Simmons said.