It was the second time in two weeks that a rocket was fired at the building, a vocational school in Miran Shah, where about seven Americans are believed to sleep during their mission with Pakistani troops in the semiautonomous area.
Earlier, they had watched a traditional Katthak dance on the lawn of a nearby fort.
The official, speaking on condition of anonymity, said the rocket was fired Friday night about 10:25 p.m. A second rocket, with a timing device set for 2:25 a.m. Saturday, was found by authorities and defused.
The first rocket hit a sports complex about 200 yards away from the school and caused little damage, the official said.
The arrival of U.S. special forces in the frontier region - off-limits usually even to the Pakistani army - has provoked protests from the fiercely independent local tribesmen.
On May 1, a rocket was fired at the same building but struck one about 300 yards away. No one was hurt in that attack, which was the first time U.S. forces have come under fire in the hostile border region since they began operations in recent weeks.
The morning after that attack, area residents found pamphlets from a previously unknown group warning that Muslims faced "disgrace and trouble" unless they "stand up against the army of Jews and Christians," and said the murder of Pakistani troops and officials assisting the Americans was also "justified."
There have been several demonstrations by tribesmen threatening violence if the U.S. forces do not leave the area.
The Pakistani government says the Americans are providing only communications and intelligence assistance, but tribesmen say they have seen American soldiers with Pakistani troops on raids of religious schools in the area.
Fourteen people, including 11 Frenchmen, were killed in a suicide bomb attack in Karachi on Wednesday.
In resoponse, Pakistani president Musharraf Saturday announced the creation of an anti-terrorism task force.
In Afghanistan itself, about 30 U.S. commandos working with 200 Afghan soldiers raided 10 houses before dawn Friday, taking nine men into custody on suspicion of aiding Taliban and al-Qaida members hiding in the former Taliban stronghold of Kandahar, police and witnesses said Saturday.
Attempts to reach spokespeople at the U.S. air base at Kandahar or the main coalition base in Bagram, north of Kabul, were not immediately successful Saturday night.
Sardar Wali, 22, said he was asleep when the American commandos and Afghan soldiers entered his family's house about 3:20 a.m. after breaking through the main gate.
"All male members of the family were searched before they threw some of them in the vehicles," he said. Six members of the family were arrested, he said. One - his 75-year-old grandfather, Saleh Mohammed - was released due to his age.
Mohammed said he was questioned for hours at the police headquarters in the presence of the Americans. "American commandos were insisting that we are supporters of al-Qaida and Taliban and that we give them shelter and money," Mohammed said.
Wali insisted it was not true. "We are not sheltering Taliban or al-Qaida people," he said.
Three men from another family were also arrested, witnesses said.
The city of Kandahar was once the power base of Mullah Mohammed Omar, the Taliban's spiritual leader, but residents say they have not seen him since he fled the city in December, promising to launch a guerrilla war against the U.S.-led forces that ousted the Taliban from power.
Meanwhile, some 600 Afghan refugees who were thwarted in their attempts to reach Australia began returning home Saturday, while about 200 Pakistani prisoners captured while fighting on the side of the Taliban were sent back to their country.
The 36 Afghans who flew home from Indonesia marked the beginning a mass repatriation of some 600 Afghans stranded in the Southeast Asian country as they tried to get to Australia to seek political asylum.
Last August, Australian Prime Minister John Howard stopped the influx of Afghans, who reached Australia on rickety boats with the help of smugglers. Those caught were sent to camps in the Pacific island nations of Nauru and Papua New Guinea.
More than 500,000 Afghan refugees have come home in the past two months, most of them from camps in neighboring Pakistan and Iran.
Also Saturday, 204 Pakistani prisoners flew home after a northern Afghan leader released them from the squalid Shibergan prison, where they had been held for nearly six months in cramped quarters and with little food.
Like 30 earlier arrivals, they were to be detained in Peshawar jail while authorities check their identities and determine whether they committed any crimes, said Attar Manilla, the provincial minister for legal affairs.