Al Jazeera's David Chater, reporting from the capital Kabul, said: "The head of the provincial council in Kandahar, President Karzai's brother, said the Afghan security forces - we believe it was the special forces under the control of the Americans in Kandahar - were stopped by the police and their vehicle taken.
"We do not know why that happened but they demanded their vehicle to be returned by the police.
"The police chief himself came down, the CID head came down, and there was a huge argument at the scene, insults were swapped and bullets started to fly.
"We don't yet know how many injured but [these were] extraordinary scenes. Afghan fighting Afghan on the streets of Kandahar, which of course had been under attack by the Taliban in recent weeks," he said.
The city in southern Afghanistan is a Taliban stronghold.
Kandahar, the birthplace of the Taliban movement in the 1990s, is in a part of Afghanistan that has seen escalating attacks by the group, which was toppled from power by US-led forces in 2001.