Extra police have been sent to the city after hundreds of far-right activists protested amid tensions over the killing of a German man for which an Iraqi and a Syrian have been arrested on charges of manslaughter.
Scuffles and pockets of violence broke out as protesters said they wanted to “show who is in charge of the city”.
Prosecutors said two men, a 23-year-old Syrian and a 22 year-old Iraqi, were taken into custody on suspicion of manslaughter after a clash on 26 August in which one man in his 30s died.
Authorities said they were still investigating a possible motive for the killing.
Both far-right and left-wing groups planned to protest Monday night, public broadcaster MDR reported.
The killing had already sparked spontaneous protests by hundreds of people in the late afternoon of 26 August in Chemnitz, a city where almost a quarter voted for the far-right Alternative für Deutschland party last year.
Videos posted on social media appeared to show far-right protesters threatening and chasing passersby on Sunday.
German government spokesman Steffen Seibert condemned the violence.
“What was seen yesterday in parts of Chemnitz and what was recorded on video has no place in our country,” Mr Seibert said.
“People ganging up, chasing people who look different from them or who come from elsewhere ... is something we won’t tolerate.
“This has no place in our cities and I can say for the German government that we condemn this in the sharpest possible manner,” he added.
Mr Seibert also criticised a far-right lawmaker who had suggested German authorities were unable to protect citizens.
“There is no place in Germany for vigilantism, for groups that want to spread hatred on the streets, for intolerance and racism,” he said.
Agencies contributed to this report
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