The Canadian, who turns 75 on Monday, was halfway through a performance of his hit song "Bird on a Wire" at a show in Valencia when he fainted.
A clip from the concert posted on YouTube showed him sitting on a platform on the stage before keeling over.
His manager later told media that the singer had suffered a bout of food poisoning but had been reluctant to abandon the show.
Organizers of his tour told the BBC that he was expected to be well enough to perform in Barcelona on Monday at the Palau Sant Jordi stadium for the final show in his nine-concert Spanish tour.
After Spain, Cohen is due to perform in Florida on October 17.
Cohen has been on tour since May, performing in Canada, Europe, New Zealand and Australia, after coming out of retirement.
He quit the music scene in the early 1990s and became a Buddhist monk but was forced out of retirement five years ago after losing his retirement savings.
He rose to fame in the 1960s with songs about sex, faith and betrayal performed in a deep baritone he once described in a song as "the gift of a golden voice." His best-known song, "Suzanne," was a hit for Judy Collins.
(Writing by Belinda Goldsmith, Editing by Bob Tourtellotte)
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