Gen. Joseph Dunford Jr.'s call took place late Thursday night, The New York Times reported.
"He talked to President Karzai directly, expressed deep regrets for the incident and any civilian casualties, and promised to convene an immediate joint investigation to determine all the facts of what happened," a coalition spokesman, who spoke anonymously, said.
The conversation came after Karzai criticized the United States for the drone attack.
He said in a statement a U.S. drone fired a missile into a house in the Helmand province, killing a 2-year-old child and wounding two women.
A coalition spokesman said Friday the attack targeted an insurgent on a motorbike but missed him and hit the civilians.
"We are aware that according to the Governor of Helmand Province that in addition to the insurgent being killed, there was one child killed and two women injured," the International Security Assistance Force said in a statement Friday. "ISAF deeply regrets any civilian casualties caused by this airstrike yesterday."
The U.S. official said the civilians were on the road at the time of the attack, not in a home.
Karzai vowed after the incident not to sign a long-term security agreement that would allow several thousand U.S. troops to stay in the country after 2014, The Washington Post said.
He had said Thursday he would cancel the agreement if one more incident killed civilians.
"For as long as such arbitrary acts and oppression of foreign forces continue, the security agreement with the United States will not be signed," Karzai said.