Dozens of other banks around the world have already been downgraded under S&P's new criteria, and several more are likely to follow.
ASB Bank, a unit of Australia's biggest bank, CBA, said S&P had not specifically identified a change in the performance of CBA or ASB as part of its review and subsequent ratings change.
ASB said the downgrade would not affect its funding costs.
The bank's general manager, treasury, Nigel Annett said the bank was well-capitalised with appropriate liquidity levels.
"We remain focused on increasing customer deposits and long term wholesale debt, and reducing our use of offshore short-term borrowing," he said in a statement.
The bank also continued to benefit from the global strength of its parent company.
"At this point we do not expect the rating adjustment to have any material impact on our funding plans or expected pricing of new issuance," he said.
"S&P has not specifically identified a change in the performance of CBA or ASB as part of its review and subsequent ratings change," he said.
ANZ's chief financial officer in Australia, Peter Marriott, said the bank remained one of a select group of banks globally that have a AA category rating under the ratings criteria.
"We continue to be regarded as amongst the strongest banks globally and with a return to the rating we held until the beginning of 2007, we are one of the few banks in the world to have come out of the global financial crisis with the same rating as we went into it with," Marriott said in a statement.
The Bank of New Zealand, a unit of National Australia Bank, said the ratings change would not have a big impact on its funding costs.
BNZ treasurer Tim Main said significant improvements have occurred since 2008 which had seen a strengthening in the bank's balance sheet.
"A higher proportion of customer deposits are now being raised and term wholesale funding has been lengthened and diversified, with a consequent reduction in short term wholesale funding," he said.
"These changes have been accelerated under the Reserve Bank of New Zealand's new liquidity policies, and in particular, under the core funding ratio that requires all banks to maintain a minimum level of stable funding to support lending assets," he said.