Ibrahimovic, who joined French giants Paris Saint-Germain from AC Milan, said, "Messi had a fantastic season but he has not won that much and he has already won the Ballon d'Or three times."
Barcelona were knocked out in the semi-finals of the Champions League by winners Chelsea while Real Madrid won the Spanish La Liga title last season.
Messi, who was named world's best player thrice, played alongside Ibrahimovic during the 2009-10 season with Barcelona. The 30-year-old PSG striker also praised his former teammates Xavi Hernandez and Andres Iniesta who won the UEFA best player award.
"It depends whether you reward an individual or a collective work," Ibrahimovic said.
"Xavi is still playing at a high level, Iniesta also had a great season, they won the Euro while Messi has not won anything, just the King's Cup. Messi has won the Ballon d'Or three times, it's now someone else's turn to win it," he said.
The Ballon d'Or, which was merged with the World Player of the Year award in 2010, will be awarded on Jan 7.