Mr Kenny criticised the decision to increase rates on all cards by up to 4% a week before Christmas.
But he said it was a commercial decision and, while the Government has a 15% stake in the bank, it has no say when it comes to setting rates.
"This is not a case of where the Government regulate the interest rates that are applicable to credit cards," Mr Kenny said. "I don't like this situation where the announcement is made by the bank applicable three or four days before Christmas, but this is a commercial entity and they have made this choice."
The bank announced an interest increase on all credit cards of between 0.7% and 4%. Customers will be hit with the hike when they get their bills in January. The changes will see fees on the bank's Classic credit rise from 17.9% to 19.9%.
Mr Kenny said that while the Government cannot dictate to the bank, it has offered the regulator in the Central Bank of Ireland more powers if he believes it appropriate.
"It's not a case of saying the Government won't do anything ," Mr Kenny said. "It's a case of saying if the regulator requires further facilities, the Government will respond to that."
Bank of Ireland announced plans to raise its fees in October, claiming it had to do so to ensure competitiveness in the market and to remain financially viable.
However, Sinn Fein president Gerry Adams accused the bank of cashing in and taking advantage of an already hard-pressed public. He appealed to Mr Kenny to do something about the unfair fee hike, suggesting he speak to the public interest directors who sit on the board of the bank.
Mr Adams accused the Taoiseach of wringing his hands and refusing to tackle the issue. He said struggling families had enough worries following the 3.5 billion euro in spending cuts and tax hikes announced in the budget earlier this month - including a new property tax due to take effect from July.