The talk show host quizzed Short on the secret to his lasting marriage with his wife Nancy, not realising that Nancy had passed away two years ago.
"You and Nancy have one of the greatest marriages of anybody in show business," Gifford told Short. "How many years now for you guys?'
Short was understandably confused, answering hesitantly: "We... have... married ... 36 years."
"Madly in love, madly in love," Short responded.
"Why?" she asked.
"Cute, I'm cute," he explained.
After the show, Gifford realised her error and tweeted an apology - to a fake Martin Short Twitter account.
"I send my sincerest apologies to @MartinShort and his family. He handled situation w/enormous grace and kindness and I'm so grateful," she wrote.
The account in question has no picture and only one tweet from 2009.
Short's wife died of natural causes in August 2010 in the wake of an ongoing battle with cancer.
Last year, the actor accepted a special honour from the Women's Research Cancer Fund on behalf of his late wife.