Protesters at the rally on Thursday accused China of orchestrating the disappearance of a Kazakh citizen and of buying up Kazakh land.
Local media and rights groups say Alimnur Turganbay has not been seen since July, when he was arrested by border officials in China's western province of Xinjiang.
Beijing has been accused for years of repressing the Muslim Uyghur minority in the province, which borders Kazakhstan.
Kazakh police said protestors at the demonstration in the Almaty region, near the border with China, had "committed unlawful acts, including the burning of the state flag and images of the leader of a foreign state".
Twelve citizens were issued short-term jail terms of up to two weeks, while six more were fined, they added.
Authorities have also opened a criminal case with potentially lengthier sentences.
A United Nations commission has said at least one million Uyghurs and other minority groups, including Kazakh citizens, have been detained in a network of camps in Xinjiang.
Beijing denies the allegations and says its actions are to counter "terrorism" and educate the population.
China is a major player across Central Asia, investing heavily in infrastructure and soft power projects in a bid to replace Russia's dominant position in the region.
The Muslim-majority Central Asian states, including Kazakhstan, have tried to largely overlook the crackdown in Xinjiang in favour of maintaining strong ties with Beijing.
An unverified video posted on Instagram showed around 30 people gathered on Thursday in an area of the Almaty region that has a large Uyghur population.
They were holding three Chinese flags and a portrait of President Xi.
"We gathered here, burned the flag and the portrait of the president of China," one unidentified protestor said in the video.
The individual accused China of holding Turganbay without cause and of buying-up Kazakh land, contravening a law against the sale of agricultural areas to foreign citizens.
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