"I think that we can all be very clear and say with a matter of fact that if you vote for Joe Biden you really are counting on a President Harris, because the idea that he would make it until 86 years old is not something that I think is likely," Ms Haley, 51, said during the news programme.
Responding to her comment, Andrew Bates, deputy press secretary at the White House, said, "As you know, we don't directly respond to campaigns from here. But honestly, I forgot she was running."
Ms Haley had launched her presidential bid around a "new generation" of leadership. She even argued that candidates above the age of 75 should take cognitive tests - a proposal slammed by US First Lady Jill Biden.
Mr Biden, meanwhile, announces his candidature on Tuesday and doesn't see his age as an issue despite several attacks from his critics.
"I can't even say - I guess, how old I am. I can't even say the number. It doesn't - it doesn't register with me. I took a hard look at it before I decided to run. And I feel good," Mr Biden told reporters on Tuesday.
Those opposed to his candidature have pointed to Mr Biden's gaffes as a sign of his declining mental health. But his campaign managers and White House officials are trying to demonstrate that Mr Biden is active and fit.
The video of his re-election campaign shows Mr Biden in his suit jacket. NBC News reported that the White House even released a spreadsheet showing Mr Biden's rigorous travel schedule in the first four months of the year, which surpasses Barack Obama's in the 2012 campaign.