Posts had been circulating on social media this week, with one Leeds councillor telling the YEP he was "inundated" with constituents telling him they had been paid twice.
The overpayment, which the council claimed was due to an "process error", means the council now has to recover £3.75m from individuals' bank accounts.
The authority has warned residents that the council would recover the amounts, and that they should not be spent.
A Leeds City Council spokesperson said: “We are aware that a significant number (25,000) of council tax rebate payments have been duplicated, meaning some residents have received the payment twice.
“This is due to a process error where the same payment file was incorrectly processed twice after it was initially rejected by the bank. We are working with our bank to recover the duplicate payments so that the situation can be rectified as soon as possible.
“We would advise residents to check relevant accounts and bear in mind that duplicate payments will be recovered.”
“We would like to apologise for any confusion or inconvenience the duplicate payments may have caused. Our officers have worked hard to ensure residents receive the £150 rebate as quickly as possible, and 120,000 payments have been made correctly.”
Households in Leeds are expected to receive more than £46m this month as part of the Government's council tax energy bills rebate scheme - with a £150 payment available to every single household in council tax band A-D.