Ibrahimovic, who retired from international football after a disappointing Swedish showing at Euro 2016, dominated the award from 2007 to 2016 and took it 11 times overall. No other player has won it more than twice.
Granqvist, Ibrahimovic's successor as captain, last week led Sweden to a 1-0 aggregate playoff victory over Italy to reach next summer's World Cup finals in Russia.
Sweden's 36-year-old record goal-scorer, who returned from serious knee injury for Manchester United against Newcastle United on Saturday, wasn't left completely empty-handed at the Fotbollsgalan awards, however.
His club performances won him the best attacker prize.
The Diamond Ball for best female player went to Linkoping FC's attacking midfielder Kosovare Asllani, who returned home this season after five years abroad with Paris Saint Germain and Manchester City.