Biden's scene with show regulars Amy Poehler and Adam Scott was shot in Washington in July at the Eisenhower Executive Office Building next to the White House, the network said.
It will air on Thursday's edition of the show.
"Vice President Biden is both Leslie's [Poehler's character] political hero and her No. 1 celebrity crush, so meeting him is obviously a huge moment for her," Mike Schur, executive producer of "Parks and Recreation," said in a statement Thursday. "We looked at a number of actors to [play] the role of 'Vice President Joe Biden,' and ultimately, Joe Biden himself gave the best audition."
"Meeting Vice President Biden was a thrill for me and for Leslie," Poehler said. "He was a good sport and a great improviser. The vice president maintained his composure while I harassed him and invaded his personal space. The nation of 'Parks and Rec' will be forever grateful."