A Taliban spokesman claimed responsibility for the assault in a phone call to Al Jazeera.
The spokesman said the Taliban was targeting Afghan intelligence because "they are slaves working for the puppet government".
US forces moved quickly to seal the area surrounding the National Directorate of Security as helicopters circled over head.
Policeman killed
Taher Khan Sabarai, the deputy governor of Khost, told Al Jazeera that some people had been killed but said he did not have details.
"One policeman was killed in the suicide blast today," Tahir Khan Sabari, the deputy provincial governor, was later quoted by the AFP news agency as saying.
"Three to four militants in army uniform also entered the building. We don't know if there was a clash or casualties inside the building or what is happening there now," he said.
Zeina Khodr, Al Jazeera's correspondent in Afghanistan, said it was the second intelligence office to come under attack in recent weeks.
"It happened in the southern city of Kandahar just three weeks ago. An apparent target was the brother of Hamid Karzai, the president of Afghanistan.
The president's brother was in a nearby building at the time but escaped unhurt.