Nobody was injured, but the attack renewed concern about Karzai's security amid militant threats to derail next month's landmark elections.
The American military said the rocket missed the chopper as it approached a landing zone near Gardez, where Karzai planned to open a school. The helicopter did not touch down and returned the president to Kabul.
"The rocket was fired at the helicopter as it was landing, and missed," U.S. military spokesman Maj. Mark McCann said. "The president was not in any imminent danger."
Presidential spokesman Jawed Ludin said the rocket came down in a village about a mile from Gardez. However, McCann and the local governor said the impact site was nearer, 300-500 yards from the landing zone.
There was no indication of who fired the rocket.
Gov. Asadullah Wafa, one of hundreds of guests who left the school without seeing the guest of honor, said police had discovered the launch site at a ruined house in a village west of Gardez but had made no arrests.
But suspicion was sure to fall on militants, including the former ruling Taliban, who are waging a stubborn insurgency against Karzai's U.S.-backed administration.
Officials are bracing for a surge in violence ahead of the Oct. 9 presidential election, which Afghanistan's international sponsors hope will cement the shaky peace process begun after the United States drove out the Taliban in 2001 for harboring Osama bin Laden.
The school opening was not officially part of Karzai's election campaign. But the attack was still a setback as he tries to muster a majority in the ballot and avoid a second-round runoff.
"He's disappointed and a little upset that the security sometimes in these situations overreacts," Ludin said. "He wished to have landed and spoken to the people."
Gardez is just 60 miles south of Kabul, but security concerns still meant Karzai needed the U.S. military as his escort.
Karzai has said he is too busy leading the country to do much campaigning, and that his two vice presidential candidates will tour the provinces in a bid to see off the electoral challenge from the 17 other candidates.
Karzai's campaign spokesman said one of his deputies would stump for votes in the northeastern Afghanistan next week and that the other would hold a rally in Kabul.
A dozen election workers already have been killed during a drive to register millions of Afghans for the country's first-ever direct presidential election.
In all, more than 900 people have died so far this year in political violence across the country.
Karzai has been constantly shadowed by Afghan and American bodyguards armed with automatic weapons since the July 2002 killing of a vice president and the September 2002 assassination attempt on the president in the southern city of Kandahar. Three people, including the gunman, died in that attack.
"I don't take it seriously at all," Karzai said at the time of the attempt. He added that he expected such attacks.
The man who fired the rifle into Kazai's car in 2002, missing the president by just inches and grazing the Kandahar governor, had been hired as a security guard just four days earlier.
The would-be assassin, who was shot dead by Karzai's American bodyguards, was from neighboring Helmand province, a former stronghold of the ousted Taliban.