Southeastern Buffalo City Metro mayor Zukiswa Ncitha, his deputy Temba Tinta and council speaker Luleka-Simon Ndzele were arrested and then later released on bail, they said.
A spokesman for the ruling African National Congress (ANC) party said up to five of its representatives, including a senior party official, had also been taken into custody.
"The arrests are in relation to the Nelson Mandela memorial saga, which is currently under investigation," the department of local government said in a statement.
They have been granted bail of USD 945 each and further hearings have been postponed to September 1 to allow time for more investigations, the police said.
Opposition parties had demanded a probe into how taxpayers' money, released for Mandela's memorial last December, had been used after allegations some of the funds had been misappropriated.
South Africa's first black president and anti-apartheid died on December 5 at the age of 95 after a long illness, prompting a global outpouring of grief.
The ANC said it had "noted the serious allegations" against the officials.
Party spokesman Keith Khoza told AFP a regional secretary was among the group of party members arrested in connection with the case.
"Corruption is a cancer that has no place in the ANC and our society," the party said in a statement.
