The gaffe was met with a bemused look by the Taoiseach and President Obama before Biden realised his mistake.
Earlier Mr Cowen had brought the vice president a bundle of shamrock and paid tribute saying the people of Ireland were proud to claim him as "one of our own".
Mr Cowen made special mention of the vice-president's mother, Jean Finnegan Biden, who died in January.
"We think of her today, and her story of dedication and service, which reflects so much about the Irish immigrant journey to these shores."
But when Mr Biden attempted to repay the compliment it went horribly wrong.
Speaking of his own Irish roots, Mr Biden tried to find a link with the Taoiseach, noting that: "His mom lived in Long Island for 10 years or so. God rest her soul."
A polite Mr Cowen stood silently at the vice president's shoulder saying nothing, until Mr Biden suddenly realised his mistake.
"Oh wait, your mom is still alive. It's your dad that passed," he said, as the room burst into laughter.
"God bless her soul," he offered by way of a revised tribute. "I got to get this straight."
Eventually Mr Biden cut his losses deciding to heed an old Irish proverb, stating: "A silent mouth is sweet to hear. Well I'm going to yield to that proverb and introduce you to the President of the United States, Barack Obama."
The St Patrick's Day faux-pas left Mr Cowen in stitches as he and President Obama laughed at Biden's poor research.
Despite the gaffe by Mr Biden, the Taoiseach's visit to the White House has been hailed as a major success. President Obama gave a fresh commitment to help reform the US immigration system, but he did not indicate whether he will travel to Ireland this year.
But the president was in jovial mood, joking about his own Irish heritage, which is linked to Moneygall in Co Offaly.
"My first thought was, 'Why didn't anyone discover this when I was running for office in Chicago?' I would have gotten here sooner," he joked.