Switzerland is not a member of NATO and has long pursued a policy of neutrality on the world stage.
Mr Biden’s blunder was immediately mocked by the Republican National Committee.
The president has made a series of verbal slips on the world stage, for example on Taiwan, some of which have raised questions about an abrupt shift in US foreign policy, only for the White House to reverse the comments.
The gaffes have led Biden’s opponents to suggest that the 79-year-old is unfit to be the leader of the free world.
Mr Biden’s presence at the three-day NATO summit in Madrid was intended to bolster the unity of the alliance, which was vilified under his predecessor, Donald Trump.
“I think we can all agree that this has been a historic NATO summit,” Biden told reporters at a closing news conference.
“This summit was about strengthening our alliances, meeting the challenges of our world as it is and the threats we will face in the future,” Biden said.
The main achievement of the three-day event was to reach an agreement between Turkey, Finland and Sweden to pave the way for the accession of Nordic countries to NATO.
Mr Biden told reporters on Thursday: “Putin wanted the ‘Finlandization’ of NATO. He got the Natoization of Finland”.