The presidential palace said in a statement that Karzai "strongly and resolutely denounces this desecrating act" and expressed "abhorrence in the face of such an insult."
The film, clips of which were disseminated by fringe Florida pastor Terry Jones, has already prompted deadly violence in Libya, where the U.S. ambassador and three other Americans were killed in an attack on the consulate in Benghazi on Tuesday. The U.S. Embassy in Cairo also came under assault.
Karzai's statement did not mention the attacks in Libya and Egypt.
Afghans tend to have hair-trigger sensibilities regarding any perceived insult to the Muslim faith. Earlier this year, the country was torn by lethal unrest after U.S. troops mistakenly burned copies of the Koran at Bagram air base, north of the capital. About three dozen people died, including four American troops.
A condemnation from Karzai was thought to have inflamed passions in the spring of 2010, after Jones and his followers staged a Koran-burning. Nearly two weeks elapsed without any reaction in Afghanistan, until Karzai issued a call for Jones' arrest and prosecution. The next day, April 1, a furious mob descended on the U.N. mission in the northern city of Mazar-e-Sharif, killing seven foreign U.N. workers.
Karzai's public stance toward the NATO force and his U.S. patrons has been somewhat hostile of late. He issued a strident statement accusing the United States of disregarding Afghan sovereignty after American authorities retained some Taliban and other insurgent suspects when handing the country's main military detention facility over to Afghan control. And the Afghan leader commemorated Tuesday's anniversary of the 9/11 attacks by criticizing the West's conduct of the war in Afghanistan.