The violence flared on Sunday as a 1000-strong group from the pro-Kurdish DEHAP party asked authorities in Batman to hand over the corpses of six Kurdistan Workers Party (PKK) rebels who had been killed in a battle with the military.
Security officials said police told the group to disperse and then intervened, firing warning shots in the air.
The dead man was killed by a stray bullet.
Police fired tear gas and water cannons into the crowd, and some protesters smashed windows and torched cars in the city's main street. Fifteen protesters were detained.
Security forces, backed by helicopters, launched an operation against PKK militants in Batman last Thursday, killing six rebels.
The fighting comes just a week after the PKK ordered its armed wing to refrain from violence for a month.
More than 30,000 people have been killed in the conflict since the PKK took up arms against the state in 1984, with the aim of carving out an ethnic homeland in southeast Turkey.
The group is viewed as a terrorist organisation by the European Union and the United States, as well as Turkey.