Police officials Monday said the rocket was fired overnight from outside Kabul and landed in the western part of the city.
A mother and father were killed along with one of their children.
Earlier, German Chancellor Angela Merkel called for a quick and thorough investigation by NATO into a German-ordered air strike in northern Afghanistan that local officials say killed civilians.
The strike Friday targeted two fuel tankers hijacked by the Taliban. But there were claims that civilians also were killed and wounded when a U.S. jet bombed the site.
German Defense Minister Franz Josef Jung defended the attack, saying the Taliban could have used the fuel tanks to launch a major attack on nearby German soldiers.
The Washington Post reported that the commander may have violated NATO rules when he ordered the air strike based on intelligence from just one source.
The newspaper says a NATO fact-finding team estimates that some 125 people were killed in the strike, and that at least 24 of them were not insurgents.
On Monday, the Afghan Rights Monitor said interviews with about 12 villagers indicate that some 60 to 70 civilians were killed and only about a dozen gunmen died in the attack.
Meanwhile, the provincial government has been giving conflicting numbers regarding the incident.
NATO rules are aimed at reducing civilian casualties, and forbid bombing civilian targets based on a sole source of information.
