A Kurdish official identified the young woman as Barin Kobani, who took part in a U.S.-backed campaign to drive the Islamic State (IS) group from the northern town of Kobane.
The Kurds in a statement blamed the "terrorist allies of the enemy Turkish state" for mutilating the body of Kobani, who was a member of the all-female Kurdish Women's Protection Units, AFP reported.
The Syrian Observatory for Human Rights, a Britain-based monitor, said it received the video from a Syrian rebel fighting with Turkish forces in the Afrin offensive.
The rebel told the Observatory the footage was filmed on Tuesday after rebels found the young woman's corpse in the village of Qurna near the Turkish border in the north of the enclave.
In the footage, a dozen men, some armed, gather around the badly mutilated body of a woman lying on the ground.
The Kurdish community reacted with outrage and social media users shared online a portrait of Kobani smiling next to another shot of her brutalized body.
"Barin did not surrender, she fought to the death," said Amad Kandal, an official with the Women's Protection Units, vowing to avenge her comrade's brutal murder.
SDF spokesman Mustefa Bali said the video of the fighter's body was reason to continue fighting back against Turkey and its allies.
"Imagine the savagery of these invaders with the bodies of our daughters. How would they behave if they took control of our neighborhoods?" he wrote on Facebook.
"All this hatred and barbarity leaves us with a single option: to continue the resistance," he said.
In a statement, the Syrian National Council, the main opposition body in exile, condemned the "criminal acts" and called for "the opening of an immediate investigation" to punish those responsible.
Turkey and allied Syrian rebels have since January 20 pressed an offensive against the Kurdish enclave of Afrin in northern Syria.
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