Nato said it was investigating the “deeply regrettable incident”.
Local Afghans have reportedly gathered near the base in Panjwai district to protest the killings, and the US embassy is advising against travel to the area.
Lt Gen Adrian Bradshaw, deputy commander of Nato-led forces, said he was unable to “explain the motivation behind such callous acts”, adding that “our thoughts and prayers are with those caught in this tragedy”.
The soldier’s name has not been released yet, but he is thought to be a staff sergeant.
“Eleven members of my family are dead. They are all dead,” Haji Samad, an elder from Najeeban village, told the AFP news agency.
Haji Sayed Jan, from Alkozai village, was quoted by the AFP as saying: “My home was attacked and I lost four family members”.
The soldier, who had reportedly suffered a breakdown before the attacks, is said to have turned himself in to US military authorities after carrying out the killings.
Last year a US soldier was convicted on three counts of premeditated murder of Afghan civilians after leading a rogue “kill team” in Afghanistan.