Mr Field said: "We received a £3.2 million grant from the EU LIFE programme to support our Saving Wildcats partnership project, which aims to restore wildcats in Scotland by breeding and releasing them into the wild.
"Wildcats are on the brink of extinction in Britain and this is the last hope for the species' survival.
"As we are no longer part of the European Union, our charity is no longer eligible to apply for funding from programmes like EU LIFE, which have proven critical for our wildlife conservation work and wider efforts to protect animals from extinction.
The zoo welcomed the birth last February of a baby chimpanzee, pictured here with mother Heleen
PA
"We have a leading conservation genetics laboratory at Edinburgh Zoo which supports conservation projects around the world, and suddenly access to both funding and other researchers for this cutting-edge science has disappeared.
"While the full impact is yet to be seen, we are also facing increased challenges around moving animals between zoos, many of which are part of important European endangered species breeding programmes."
The programme is currently about £900,000 short, meaning it may have to be cancelled.
Mr Field said: "We still need to reduce costs to secure our future. It may be that some of our incredibly important conservation projects, including the vital lifeline for Scotland's wildcats, may have to be deferred, postponed or even stopped.
"Yang Guang and Tian Tian have made a tremendous impression on our visitors over the last nine years, helping millions of people connect to nature and inspiring them to take an interest in wildlife conservation.
"I would love for them to be able to stay for a few more years with us and that is certainly my current aim."
