The dog section is set to merge with Humberside Police’s as part of cuts to the force’s Operational Support Services.
The new, merged unit will be based at Niagara in Sheffield.
It means there will only be 25 police dogs to cover the whole of South Yorkshire and Humberside.
South Yorkshire Police has lost 75 per cent of its dog handlers and dogs since March 2014. The number was originally cut from 48 to 24.
A further 12 posts are to be cut from April 2016 – leaving just 12 dog handlers to cover events such as football matches and demonstrations as well as carry out regular policing duties such as pursuing suspects and searching properties.
It is understood the force’s existing dog handlers will have to apply for their own jobs and will be assessed on their experience, attendance, amount of training they have received, the age of the dog and how proactive the officers are.
Neil Bowles, chairman of South Yorkshire branch of the Police Federation, said: “Officers are very angry about it. We have been consulted but they took no notice of what we said and senior officers have agreed the plan.
“It means our officers could be called to jobs in Bridlington but if a search is required the scent will have gone by the time they get there.
“All our frontline officers are aghast because everyone knows police dogs are an extremely valuable resource and can quell a riot.
“They cover football matches and marches and it’s going to mean an increased chance of cancelled rest days for the handlers who are left, so that will have an impact.
“There won’t be as many to cover normal jobs such as searching properties, looking for missing people and finding criminals who have gone to ground after a chase – it all has a knock on effect.”
Mr Bowles blamed the Government for slashing police budgets.
A force spokeswoman said: “South Yorkshire Police is to restructure the size of its dog section as the force merges with Humberside’s dog section, as part of the substantial savings to be achieved, that are required to meet budgetary cuts imposed on the Force’s Operational Support Services.
“It is part of a wider programme of change taking place throughout the force to ensure the police continue to provide the best possible public service but within a significantly reduced budget.
“A number of dog handler posts will be lost through natural retirement, however cover will still be provided to both counties 24 hours a day, seven days a week. Police dogs and their handlers provide a range of important roles in helping to keep the public safe.”