When one antelope in the zoo died of the disease in May last year, 11 other were culled.
The zoo has reinforced fencing around the perimeter of the grounds to attempt to keep out badgers, which are thought to have introduced the disease to the facility, a staff said.
Now, vets fear the zoo could run out of space and they are trying to restrict reproduction by using contraception such as injections, tablets, implants and IUD coils.
Five-year-old lioness Maliya was among those given an implant under a general anesthetic.
Maliya and male Lucifer are endangered Asiatic lions and expected to breed to boost the population.
Simon Tonge, the Executive Director of the zoo, said it was "frustrating" the contraceptive programme was put on hold.
"Even a single positive case of TB leads to movement restrictions on mammals. This prevents us from being able to move young mammals on to other collections, hence the need to curtail breeding," he told the Independent.
"There are lots of fit and healthy breeding animals here, representatives of rare and endangered species, many of which, like the Asiatic lions, are part of international efforts to conserve their species. Maliya and Lucifer are the second most important breeding pair in Europe.
Tonge said the zoo hoped to lift the TB-related restrictions soon but was acting under the direction of the Department for Environment, Food and Rural Affairs.
Senior Head Keeper of Mammals, Rob Rouse, said: "We need to be responsible for managing the space we have so we don't run out of the room."(ANI)