Solly Msimanga, from the opposition Democratic Alliance (DA), said the vehicles would instead be given to a police anti-hijack unit.
However, he will continue to use the luxury car used by the previous mayor.
The DA took control of Tshwane, a metropolitan area including the capital Pretoria, from the African National Congress (ANC) in local elections.
Mr Msimanga said no more luxury cars would be bought under his leadership.
He took over from the governing ANC, which lost control of the capital for the first time since 1994, last month.
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The ANC bought 10 new BMW 3 series vehicles, which are yet to be delivered, for 5 million rand ($356,000; £266,000), local reports say.
The cars were meant for members of the mayoral council, with the ANC said to be confident it would retain control of the municipality in the elections.
Solly MsimangaImage copyrightEPA
Image caption
Solly Msimanga won elections in August
He will still use a BMW 5 series car he inherited from the previous mayor, reports the IOL website.
Mr Msimanga's spokesman Matthew Gerstner told the BBC that this vehicle could not "be dispensed with because it's been bought and paid for already and treasury regulations prohibit that".
He added: "But, as soon as he can replace it, he will, with a sensible, low-cost vehicle".
Mr Msimango says the DA-led coalition government wanted to embark on cost-cutting measures.
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Media captionThe ruling African National Congress has got the lowest share of the vote since 1994
He said in a statement: "No new luxury cars will be bought or leased for politicians‚ and if vehicles currently owned by Tshwane require replacement‚ sensible and low-cost vehicles will be procured.
"I will not allow public money to be spent on luxury cars‚ while our people struggle for services‚ houses and jobs.
"A Hyundai i20 or Toyota Corolla can do the same job for a politician as an expensive sedan."
The ANC national government has been criticised for wasteful expenditure, so South Africans will be closely watching what the opposition do differently in the key urban areas they won in the August elections, says the BBC's Pumza Fihlani in Johannesburg.
South Africans will be keen to see if the opposition, which has until now only run one province, will be able to make good on its ambitious election promises, our correspondent says.