Local officials say the incident took place late on April 17.
The governor of Khost Province, Mayrajuddin Patan, told RFE/RL's Radio Free Afghanistan that the U.S. patrol opened fire on the car after it ignored instructions to stop.
"Reports of some news agencies, particularly Khybar TV, that American forces killed seven civilians, are false and based on rumors," Patan said. "What really happened is that U.S. forces patrolling at night ordered a car to stop, but the car didn't stop.[U.S. soldiers] thought that those people might be terrorists and a soldier fired one bullet and that one bullet injured three people. It was really an accident."
Some reports say up to six civilians were injured, including a baby.
In another part of Khost, a 5-year-old boy and another youngster were wounded by U.S.-led troops on April 18.
There has been no response from the U.S. military in Afghanistan.
The incidents took place after President Hamid Karzai had urged U.S.-led coalition forces to show restraint when attacking militants in order to avoid civilian casualties.