"Three people died," an official in Changsha, the capital of Hunan province, told AFP by phone. "I can assure you it's not a terror attack. It happened in a market due to some dispute."
The official news agency Xinhua reported that "a group of knife-wielding assailants attacked civilians" and left "three bodies lying on the ground".
Police and ambulances had arrived and the area had been cordoned off, it added.
A Hunan radio station described one attacker, who ran a bakery, as having a dispute and then stabbing to death a woman in her 80s who had just walked out onto the street.
Three people had been killed and one injured, it said on its account of Sina Weibo, a Chinese version of Twitter, citing police.
The Hunan Daily newspaper said, citing an eyewitness, that one male had a dispute with another, attacked him with a kitchen knife, and then ran after other people until altogether "five passersby were stabbed".
Photos posted online -- whose authenticity could not be verified -- appeared to show the bloodied bodies of three men lying on the ground, with armed police and bystanders nearby. Another showed a man being taken away by officers.
Internet users quoted by news services said one attacker had been shot dead by police.
The incident came after attackers launched a stabbing spree in the southwestern city of Kunming in Yunnan province on March 1, leaving 29 people dead and 143 wounded in what domestic media have dubbed China's "9/11".
Authorities blamed that "terrorist" incident on militants from the restive far-west region of Xinjiang, home to the mainly Muslim Uighur ethnic minority.
Knife and bomb attacks by Uighurs are reported periodically in Xinjiang, usually targeting police or government officials and labelled by authorities as terrorist attacks.
Rights group say the unrest stems from harsh cultural and religious repression, while Beijing says it faces a violent separatist movement motivated by religious extremism.
In the Kunming attack, which took place at a rail station, four assailants were shot dead at the scene, one was detained on site and three others were arrested separately.