Several men and women burst into the south-western city’s railway station stabbing people at random, leaving 29 dead and wounding more than 130.
Officials have blamed separatists from the Xinjiang region for the attack.
Four attackers were shot dead by police at the scene, officials say. An injured female suspect was reportedly detained.
Citing a statement from the Ministry of Public Security, Xinhua news agency said six men and two women, led by a person identified as Abdurehim Kurban, were responsible for the attack.
There were no details about how the suspects were identified and captured.
Officials say that evidence, such as insignia recovered from the station about “East Turkestan”, points to the involvement of separatists from Xinjiang – a region in the far west of China bordering Central Asia.
China’s security chief, Meng Jianzhu, has vowed “all-out efforts” to “severely punish terrorists”.
Eyewitnesses described horrific scenes on Saturday, saying that in just 12 minutes attackers used curved swords and meat cleavers to stab people at random as they rampaged through the station.
A memorial for the victims has been set up at Kunming station’s concourse
Kunming is the capital of China’s Yunnan province. On Monday, security was tight, with a heavy police presence at Kunming station and surrounding areas.
Xinjiang is home to the Muslim Uighur minority group. Recent months have seen several violent incidents there which the government has blamed on extremists. Verifying these reports is difficult because foreign journalists’ access to the region is tightly controlled.
China is often accused of exaggerating the threat of Islamist terrorism to justify its harsh security crackdown in Xinjiang and the restrictions it places on the religion and culture of the Uighurs.
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