Some Afghan witnesses and officials, including Afghanistan's ministry of education, accused a US soldier of throwing the grenade.
Several witnesses and victims wounded in the blast told said that they had seen a US soldier fire a grenade-launching weapon.
Others said they saw a soldier reach into his pocket and throw a grenade.
Ehsanullah Fazli, a doctor at the Asadabad hospital, said most of the people wounded in the blast were children and some were in a critical condition.
Karzai ordered his ministry of interior and local government officials to dispatch a "high-ranking delegation" to investigate.
Karzai did not explicitly blame US forces for causing the deaths and injuries, but he said American forces needed to be careful around civilians.
"Stressing the need to protect the lives and property of civilians, President Karzai once again reminded the international forces to make every effort to avoid incidents that lead to civilian casualties," He said in a statement.
US military on Youtube
US military officials and the ministry of interior said fragments from a Russian-made grenade were found at the site, and blamed someone in the crowd for throwing the munition.
None of the half dozen US soldiers in the video can be seen throwing a grenade.
The US military said the video was taken by a stationary aerial balloon with a camera attached to it.
The military, which has increased its use of social networking sites in recent weeks, released the video on Facebook and YouTube.