The volunteers said the attackers shouted "Go back to your America!" during the rampage.
Ultra-nationalists, state media and officials in Russia often paint environmental groups like Greenpeace as traitors and spies, part of a pro-Western "fifth column" seeking to undermine the country.
Grigory Kuksin, who led the Greenpeace group, wrote in a statement that the attackers had forced him to lie on the ground while they fired shots close to his head. The men sprayed "Pedophiles here" on the camp's gates. A spokesperson said it was the most violent attack on a Greenpeace expedition in Russia that they could remember.
The Greenpeace volunteers were in the Kuban region helping local fire services battle grass fires and also educating local groups in fire prevention, an expedition a Greenpeace spokesman said had previously been carried out elsewhere without trouble.
Local police have opened a criminal investigation into the assault, the Interfax news agency reported, saying officers were working to identify those involved.
On Thursday, the Cossacks blocked the Greenpeace camp for hours, preventing the volunteers from leaving and heckling them, the organization said.
Cossack groups in the Kuban region have recently been involved in a series of politically-motivated assaults, punching and whipping a group of opposition activists when they visited the area. Local authorities have previously hired the groups to work as neighborhood patrols.
A spokesperson for Greenpeace, Halimat Tekeeva, declined to say whether the group believed the masked attackers were connected to the Cossacks and suggested the assault, though nationalist-themed, may also have a financial motive. So far, the spokesperson said, the group remains unsure of the motives behind the attack.
"I think it’s an absurd situation," Tekeeva said, adding that the volunteers sole purpose had been to fight fires. "Most people there are very glad to see us, including the state firefighters. I think it’s something to do with a specific group of people with some sort of specific interests there. But what exactly we don’t know yet.”