Leno displayed a photo of Mr Cowen and asked his audience to guess if he was a bartender, a politician or a "nightclub comedian", before revealing he was the "Prime Minister of Ireland" to loud laughter.
"He's Brian Cowen, the Prime Minister of Ireland. Oh God, it's so nice to know we're not the only country with drunken morons, isn't it?" Leno joked.
An NBC spokeswoman refused to comment after being asked whether Leno would apologise for his remarks about Mr Cowen. But a source on the 'Tonight' show described it as a comedy show that reflected current events.
"We don't comment on the jokes made on the programme," the source added.
But Leno's comments were condemned by the head of the Oireachtas Communications Committee, Fianna Fail TD MJ Nolan. He said Leno had a responsibility to have "fair comment" on his show.
"Politicians these days are the butt of a lot of entertainers' comments. I would prefer if the comment wasn't made," he said.
The ' Tonight Show' has an audience of 4.1 million people in the US and is also watched by people around the world when it is repeated on the CNBC satellite channel several days later. The sketch was broadcast during an episode of the show last week. Mr Nolan said bad publicity about the State in the international media was being watched by overseas bankers and seemed to be having a negative impact on the rates the State was paying to borrow money.
"It's obviously a very popular programme in the States and it's not the type of publicity we want for us in the current climate when we're trying to do everything to improve our image internationally," he said.
The Department of the Taoiseach did not respond last night to the comments made by Leno about Mr Cowen.
Leno has apologised on a number of occasions in the past to people who were offended by jokes made on his show.
In 2008, he apologised to Ryan Philippe after his demand for the actor's 'gayest look' was criticised by gay activists. In 2006, he was forced to say sorry to the survivor of a gun attack after using footage of his ordeal to make a joke about former US president Dick Cheney's accidental shooting of a friend on a hunting expedition.
Mr Cowen has featured in the international media since it emerged he was singing and drinking in the early hours of the morning at the Fianna Fail party think-in in the Ardilaun Hotel, Co Galway, two weeks ago.
He was criticised for his performance on an RTE 'Morning Ireland' interview several hours later. He admitted afterwards that he needed to be more cautious in his social life but strongly denied he was drunk or hungover during the interview.