The International Security Assistance Force said three coalition members and a civilian translator died in the blast, but didn't specify the location of the blast or provide other information in its release.
However, The New York Times reported the suicide bombing occurred in a gathering place as the patrol walked by, and 16 Afghan police officers and civilians were killed in addition to the three ISAF soldiers and translator.
Six police officers were among the dead and 59 Afghans were among the injured, provincial officials said.
The Taliban claimed responsibility for the attack.
"A foreign and Afghan force joint convoy was targeted this morning ... in the vicinity of the Khost governor's office, while the soldiers were dismounted in the area," the Taliban said in a statement released to the media.
Local officials said it was the third time in which targets were in the city of Khost, the capital of the eastern province of the same name.
One witness, a shopkeeper, told the Times the coalition and Afghan troops were approaching his shop "when we heard a really loud bang, followed by gunfire."
"A big ball of gray smoke went into the air," the shopkeeper said. "People in the bazaar started running away from the blast site. We all hurriedly closed our shops and ran away."