It follows similar moves by Bristol, Sunderland and several other towns and cities in the last few weeks.
Fish have traditionally been given out at funfairs to children for winning games at the stalls.
But the RSPCA has called the practice "cruel and outdated" and started a campaign to ban it earlier this summer.
Wakefield first took steps towards outlawing pets for prizes at a local level in 2008, by making changes to their licensing system.
But a motion passed on Wednesday, which was backed by all councillors, will tighten the rules further.
Liberal Democrat Tom Gordon, who put forward the motion, said: "Sadly, there's no fun at the fair for the animals who are given away as prizes.
"These are often goldfish and they're in plastic bags for long periods of time that are poorly oxygenated and they can die from temperature changes.
"That's before they even get home, where many people aren't prepared to maintain or look after a new pet.
"People wouldn't accept cats being given away as pets at the fairground, but for goldfish it's still very common and there's no law across England and Wales against it.
"While people may win at the fair, the pets are certainly the losers."
Councillors from all sides supported the ban unanimously.
Nic Stansby: "When I was younger I actually won a goldfish at Hull Fair.
"I took it home as a pet and it meant a lot to me.
"But in this instance, times have changed."
Local Democracy Reporting Service