Police, who told people to stay in their homes, named the suspect as 22-year-old Syrian Jaber Albakr. Photographs posted on social media showed armed police clad in black balaclavas and helmets at an apartment building in the eastern city.
Germany has been on edge after suffering two attacks claimed by the Islamic State group (IS) in July -- an axe rampage on a train in Wuerzburg that injured five and a suicide bombing in Ansbach that left 15 wounded.
They said Albakr was wearing a black hooded sweatshirt and was "suspected of preparing a bomb attack".
A search of an apartment in Chemnitz detected traces of explosives but failed to capture the suspect or find a bomb, a police spokesman said.
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He said police launched Saturday's operation after receiving information from domestic intelligence services.
"We are carrying out in Chemnitz a large-scale operation due to suspicions that a bomb attack was being prepared," police said on Twitter, urging residents to stay at home.
The attacks in July rattled Germans' sense of security and fuelled concerns over the country's record influx of migrants and refugees last year.
German police said previously they had identified 523 people who posed a security threat to the country, around half of whom were known to be currently in Germany.
On September 21 German officials said a 16-year-old Syrian refugee had been arrested on suspicion of planning a bomb attack in the name of IS.
The youngster, thought to have been radicalised only recently, was detained in a special forces operation at a shelter for asylum-seekers in the western city of Cologne, police and prosecutors said.
A week earlier, German police detained three men with forged Syrian passports accused of being IS militants and labelled a possible "sleeper cell" with links to the assailants behind the November attacks in Paris.