The new policy prevents pets of any kind being offered as prizes at all types of events, and also applies to council-owned buildings.
Anyone caught breaching the rule will be evicted and have their licence or hire agreement revoked.
The ban was put forward at a meeting of the council’s cabinet following a campaign by the RSPCA.
Members also resolved to lobby the government to make the “out-dated” practice illegal across the country.
Councillor Dean Carroll, portfolio holder for highways and physical infrastructure, said: “This came to our attention last year when a number of residents contacted local councillors, myself included, to raise awareness of the RSPCA campaign to abolish the practice of giving pets as prizes.
“I think most people will be familiar from childhood with the practice, particularly at fairgrounds, of goldfish in plastic bags of water being handed out to often quite bemused children for prizes at various stalls.
“What we now know is that that practice is extremely harmful and distressing to the animals.
“They are often received by families who had no intention that morning of going home with a pet, and have none of the equipment or knowledge necessary for taking care of that pet.
“In fact quite often those pets don’t even make it home due to the psychological trauma, lack of oxygen from being kept in a sealed plastic bag, or sudden change in temperature from hanging up outside in the direct sunlight to then being put in a car with air conditioning for a long drive home.
“There’s also the other unfortunate impact that some people acquiring these prizes with no intention of keeping them release them into the wild, into a watercourse or even flushed down the toilet sadly.
“With small mammals, they can be released into a field and this has dire biodiversity effects on the ecosystems that they are released into in which they are not part of the natural environment.”
Councillor Carroll said he was pleased to recommend that cabinet impose an immediate ban, as suggested in a report to members by Mark Barrow, director of place.
This will be achieved through adapting the council’s current licensing and lease agreements.
Councillor Carroll added: “We will also be petitioning the government to request an outright ban on giving live animals as prizes on all land within the UK.”
Cabinet unanimously voted in favour of ban.
Mr Barrow’s report said a number of other councils across the country had already taken the step, including Caerphilly, the Vale of Glamorgan, Torridge, Sunderland, Stevenage and the London Assembly.
He also said that while no such ban had yet been tested in law, the council has set a precedent regarding other practices “that are detrimental to the environment and the welfare of people and animals”, by implementing a ban on the release of sky/Chinese lanterns in 2018.