The Daily Show is one of the most popular programmes on US television, attracting around 1.5 milion viewers. Löfven, who is on an official visit in the United States, has been interviewed for the show.
Löfven is not the first Social Democrat politician to appear on the Daily Show. Leif Pagrotsky, a Social Democrat who has held several ministerial posts, was on it in 2009.
The last time a Swede participated in the programme was in September, when author and journalist Jenny Nordberg was invited to speak about her book The Underground Girls of Kabul. Löfven, however, will not be a studio guest.
During his visit in New York City, Löfven has met with Hillary Clinton to discuss Sweden's contribution to international security and gender issues. He also held meetings with United Nations Secretary- General Ban-Ki Moon and Deputy Secretary-General Jan Eliasson.
Löfven's tour has also included a meeting with former New York City mayor Michael Bloomberg, a lecture at New York University, a visit to the New York office of Swedish music-streaming service Spotify and a tour of a school in the Bronx.
Löfven told news agency TT that he was impressed by the diversity at the school, which focuses on science. He said: "The pupils themselves talk about diversity, about how they complement each other. One plus one becomes more than two, it is three or four."