Ibrahimovic won a fans' online vote to get the Puskas Award for best goal, a long-range bicycle kick for Sweden against England in a November 2012 friendly.
Blatter, an International Olympic Committee member, gave his presidential award to Jacques Rogge, the IOC President for 12 years until reaching his term limit last September.
The Afghanistan football federation got the fair play award after hosting its first international match in more than a decade.
Pele, viewed by many as the greatest footballer ever, finally received a Ballon d'Or trophy which he could never get during his career when the original prize created by France Football magazine in 1956 was restricted to European players.
The only player to win the World Cup three times - in 1958, `62 and `70 - was given a standing ovation at the Zurich Kongresshaus.
"I promised my family I would not cry but I am emotional," Pele said. "Thank God, I complete my trophies at home."