Dawood Ahmadi, a spokesman for the provincial government, said the alliance launched the airstrike late on Saturday in retaliation for an attack earlier in the day on a US Marine base in Helmand's northwest district of Nawzad.
He said Nato hit two civilian houses, killing five girls, seven boys and two women. Male relatives cradled the bodies of several young children, who were wrapped in bloody sheets and placed side to side. They brought them in the back of a truck to the provincial capital, Lashkar Gah.
"My house was bombarded in the middle of the night and my children were killed … the Taleban were far away from my home. Why was my house bombed?" Noor Agha, a relative of one of those killed, asked.
Mr Karzai blamed US troops for the airstrikes, in which six other civilians were wounded.
The president has repeatedly called on coalition forces to minimise night raids and airstrikes, and to clear the operations with his forces.
"We have told the Americans and Nato forces several times that unco-ordinated operations will result in the killing of innocent civilians and that such operations are inhumane, but still no-one has listened," Mr Karzai said last night.
He added that his condemnation would be "the last warning to Nato forces, American forces, and American officials".
Nato spokesman Major Tim James said a joint coalition and Afghan delegation was travelling last night to the site to investigate. He did not confirm the airstrike and provided no details about it, or about the earlier attack on the Marines.
Civilian deaths are a constant source of tension between Nato and Afghan officials.
Helmand borders Pakistan and is an insurgent bastion. The province's vast poppy fields are the Taleban's prime profit centre.
Afghan insurgents have stepped up a spring offensive across the country.
The Afghan public, which has grown increasingly hostile to foreigners as the nearly decade-long war continues, tends to perceive the Nato raids as capturing the wrong people or mistreating civilians during searches of private homes and compounds.
The latest civilian casualties are likely to add to the hostility.
The air strike comes days after protests by thousands of people against a night raid by Nato troops in which four people, including two women, were killed.
Twelve people were killed during those protests and in clashes with police in Takhar. More than 80 were wounded.
In February, four days of operations by Afghan and foreign troops killed 64 civilians in the eastern Kunar province, Afghan officials said, including many women and children.A Nato rocket attack last July killed 39 civilians, almost all women or children, in Helmand.
On Saturday, Mr Karzai ordered the Defence Ministry to take control of the night raids, saying Afghan troops should be carrying out the sensitive operations themselves.
Afghans claim that the raids, carried out on houses suspected of harbouring insurgents, often lead to civilian casualties.
Under a plan agreed by Nato leaders, foreign troops will begin handing over security responsibilities to Afghan troops from July, with a plan to withdraw all combat troops from Afghanistan by the end of 2014.