Biden will lead the delegation. Georgetown University President John J. DeGioia will also be in the delegation.
Francis was named pope on Wednesday. Soon after the White House announced that it would send a delegation to the celebratory mass, to take place on March 19.
House Speaker John Boehner (R-Ohio), on Thursday, declined an invitation to join the delegation.
"Unfortunately, my duties in the House next week — including hosting President Obama and the Prime Minister of Ireland at the Capitol on Tuesday, and the debate on the budget — make that impossible," Boehner said in a statement. "I wish the Vice President all the best in his journey, and hope he communicates the prayers and warm regards of every American, especially Catholics, to the first pope from the Americas."
Martinez, considered one of the GOP's top Hispanic stars, was mentioned as a possible vice presidential candidate for Mitt Romney during the 2012 presidential campaign.