The film was dedicated to Gerald Durrell and Peter Cook. Some scenes were filmed at Jersey Zoo, a zoological park founded by Durrell.
The film opens with Willa Weston (Jamie Lee Curtis) arriving in Atlanta to take a high ranking position in a company recently acquired by Octopus Inc.'s owner, Rod McCain (Kevin Kline). But Rod informs her that he has already sold the company where she was to work. Willa then agrees to run another recent acquisition, Marwood Zoo, in an attempt to create a business model that can be used for multiple zoos in the future. Rod McCain's son Vincent (Kevin Kline), who feels an unreciprocated attraction to Willa, announces that he will join her at the zoo.
The newly appointed director of the zoo is a retired Hong Kong Police Force officer and former Octopus Television employee, Rollo Lee (John Cleese). In order to meet Octopus's revenue target of 20% from all assets, Rollo institutes a "fierce creatures" theme on the assumption that dangerous and violent animals will attract more visitors. All animals not meeting those requirements must go. All the animal keepers, including spider-handler Bugsy (Michael Palin), make various attempts to get Rollo to change his mind. One of which is getting Rollo to exterminate five cute animals himself. But Rollo, seeing through their prank, fakes the animals' extermination. Rolls keeps the animals in his bedroom which later caused Willa and Vincent to misunderstand that Rollo is having sex orgy with female staff.
Rollo discovers that several staffs are faking horrific animal attack injuries. Rollo fires several warning shots at those responsible and Reggae (Ronnie Corbett) rushed in, mistook one of them is shot. Rollo then finds a visitor who has had a genuine accident but, not believing it is real, tastes the blood of the visitor whilst loudly proclaiming that it is fake. Just then Willa and Vincent arrive and this fiasco sees Rollo demoted to middle management. Vince even threatens to fire him if his apparent activities with female staff do not cease.
Vince covers zoo and animals alike with advertisements after secretly garnering sponsors; dresses the staff in ridiculous outfits and installs an artificial panda in one the enclosures. His continued attempts to seduce Willa fail, while she comes to enjoy working at the zoo, after having a close encounter with a silver-back gorilla. She finds herself attracted to Rollo after becoming fascinated by his apparent ability to attract multiple women. When Rollo attempts to have a discussion about Vince's marketing plan, she suggests they have dinner. But she is forced to postpone when she remembers Rod is coming from Atlanta to discuss the running of the zoo.
Worried that the visit may be part of a plan to close the zoo, Rollo and the zookeepers quickly bug Rod's hotel room to find out. Although the plan goes awry, they learn that Rod wants to turn over the zoo to the Japanese to make a golf-course and is not intending to die.
Upon discovering that Vince has stolen sponsorship money he raised, Willa warns him to return it, or else, she will tell Rod. When Rollo attempts to work out how the theft can be traced,he and Willa finally kiss, just as Vince arrives to return the money. A confrontation takes place first at the zoo office, and then outside as Willa, Rollo, Bugsy and several others attempt to stop Vince from running off with the money. Bugsy refuses to shut up, so Vince loses his temper and grabs a pistol from the management office. Rod arrives just as Vince is being subdued and announces the police are on their way to arrest Vince for stealing. Vince tries and fails to shoot his father, but then Bugsy takes the pistol and accidentally shoots Rod between the eyes.
In the panic that follows, a plan emerges to fool Neville (Bille Brown) and the arriving police. The keepers work together to dress Vince up as Rod, since he can imitate his father's accent fairly well. When the police and Neville arrive, Vince (as Rod) tells them that he has re-written Rod's will, specifying that the zoo will become a trust of the caretakers while Vince will inherit everything else, and he wants all of them to be witnesses. After signing the new will, Vince locks himself in a caretaker hut where he feigns Rod's suicide. Although Neville becomes suspicious, he is left dumbstruck when he discovers the dead body of his boss in the hut (and Vince promptly fires him before he can recover).
Now free, the zookeepers destroy the evidence of McCain's ownership. Vince becomes the new CEO of Octopus, while Willa and Rollo happily begin a new life together continuing to run the zoo.John Cleese as Rollo Lee
Jamie Lee Curtis as Willa Weston
Kevin Kline as Rod McCain/Vince McCain
Michael Palin as Adrian 'Bugsy' Malone
Robert Lindsay as Sydney Lotterby
Ronnie Corbett as Reggie Sea Lions
Carey Lowell as Cub Felines
Bille Brown as Neville
Derek Griffiths as Gerry Ungulates
Maria Aitken as Di Harding
Cynthia Cleese as Pip Small Mammals
Richard Ridings as Hugh Primates
Gareth Hunt as Inspector Masefield
Cleese began writing the script in 1992 and shooting began on 15 May 1995. It completed in August and the film was previewed in November of that year. Preview audiences expressed dissatisfaction with the ending, and in February 1996 the decision was made to reshoot the ending and some other sequences. These additional scenes could not be shot until August 1996 because of the availability of the cast, in particular Michael Palin who was making Full Circle. In the meantime, Cleese and Johnstone worked on a new ending with William Goldman. The delay meant that director Robert Young was busy on pre production for Jane Eyre so Cleese hired Fred Schepisi, with whom he had been discussing making a version of Don Quixote. The reshoots took five weeks and cost $7 million.
Schepisi claims he tried to get the producers take out the opening 15 minutes, which was done for a test screening, but then some of this footage was put back in, which Schepisi thought killed the movie.
Reviews were mixed, as Fierce Creatures holds a 53% rating on Rotten Tomatoes from a sample of 32 critics.
Roger Ebert awarded the film two and a half out of four stars, and compared it unfavourably to A Fish Called Wanda, writing: "It lacks the hair-trigger timing, the headlong rush into comic illogic, that made Wanda so special."
Cleese has since stated that following up A Fish Called Wanda with a second film had been a mistake. When asked in 2008 by his friend, director and restaurant critic Michael Winner what he would do differently if he could live his life again, Cleese responded, "I wouldn't have married Alyce Faye Eichelberger and I wouldn't have made Fierce Creatures."