The suspect who remains at large, 22-year-old Syrian Jaber Albakr, could have had "an Islamist motive" sources close to the police told AFP.
"Highly explosive materials were found in the apartment concerned in Chemnitz, new evacuation measures are necessary," tweeted police in Germany's east.
Officers found "several hundred grams (of a) very dangerous substance which cannot be moved without protective measures", said police spokesman Tom Bernhardt.
Two of those arrested were seized close to the city's railway station while the other was taken into custody in the city centre. A package belonging to one of those arrested was undergoing analysis, police added.
"They were known to the suspect we are looking for and were arrested and detained," said Bernhardt who added that the trio were being questioned.
Germany has been on edge after suffering two attacks claimed by the Islamic State group (ISIL/ISIS/IS/Daesh) in July -- an axe rampage on a train in Wuerzburg that injured five and a suicide bombing in Ansbach that left 15 wounded.
The attacks in July rattled Germans' sense of security and fuelled concerns over the country's record influx of migrants and refugees last year.
Police in the state of Saxony, where Chemnitz is located, issued a search warrant for Albakr after officers received information from domestic intelligence services, a police spokesman said, saying he was born in Syria in January 1994.
They added that Albakr was wearing a black hooded sweatshirt and was "suspected of preparing a bomb attack" and issued an image of the man.
He arrived in Germany as a refugee last year and was under interior ministry surveillance for a period, according to Focus magazine, which cited intelligence sources.
The German magazine's website added that he had been plotting to attack an airport in the country.
A vast police operation was underway as heavily armed officers, some wearing balaclavas, combed the area around Albakr's apartment and local residents were evacuated.
An explosion was heard in the leafy Chemnitz suburb which investigators said was a police entry device.
Part of the city's main station was sealed off by officers as a remote-controlled robot was deployed to inspect a suspect package on a platform.
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.
Initial information gathered from the teenager's mobile phone showed that he had expressed an "unmistakeable willingness" to carry out an attack, Klaus-Stephan Becker of the Cologne police told reporters.
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.
More than 200 police took part in pre-dawn raids in northern Germany to detain the men, suspected of either plotting an attack or awaiting orders to commit one.
German authorities have urged the public not to confuse migrants with "terrorists", but have acknowledged that more terrorists may have entered the country among the one million asylum-seekers who arrived last year; AFP reported.
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